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Have you found your heater growing cold, first on one side of the car and then on the other? As long as the heater core isn’t damaged or leaking, it can be flushed. BUT… BE CAREFUL! Many YouTubers recommend pressurizing the core with a garden hose or compressed-air as the first step. That could easily burst the fragile aluminum core (especially if weakened by corrosion) or blow one of the rubber o-ring seals inside the dash.
If that happens, allow me to refer you to the DIY from hell… E90 Heater Core DIY
This DIY heater core replacement is incredibly well documented, but the work is difficult and takes days - or thousands of dollars to have this done by a dealer or mechanic.

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For most BMW E9x models/options, the heater core circulates coolant full-time, while the blend doors/flaps inside the car direct hot or cold air into the cabin.

A gentler and more calculated approach to flushing sediment is especially important in this engine, because of the possibility of oil contamination in the coolant.
The notoriously flimsy Oil Fiter Housing Gasket separates engine oil from coolant, both of which are pressurized in the engine. When that gasket fails (and it will), oil often leaks into the cooling system, perhaps very slowly at first.
When oil reacts with coolant, it forms gelatinous blobs of sludge that collect everywhere in the system. That sludge may be relatively colorless at first, but it is highly corrosive to ALL of the plastic and rubber parts in the cooling system. It also blocks passages and is exceedingly difficult to remove. I discovered that radiator flush products do not budge it. The only thing that worked successfully, was filling the cooling system with a 50/50 mix of SuperClean degreaser and distilled water, then running the car up to operating temp before draining and repeating the process several times. Gobs of sludge came out each time, but the heater core did not clear, and within a year, it was totally blocked and freezing cold.

The potential for oil in the coolant is highly relevant to the heater core flush procedure below. Several reputable mechanics recommend this method as the best procedure to treat any blocked heater core because it works first on oil/grease deposits (which bind the sediments in the core), then on corrosion/scale deposits. Only then, should the loose material be gently blasted out. It worked wonders for my car and saved me a fortune.

Note that it is wise to replace the coolant after flushing a blocked core because the old coolant may be contaminated and circulating muck throughout the system.
If sludge is found in the cooling system, it would also be wise to do a flush of the entire cooling system and replace any plastic parts, rubber seals or hoses affected by oil contamination while you're working in that area.
Always monitor the health of your oil filter housing gaskets and replace them preemptively to avoid expensive repairs!

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• Start by draining the coolant.
• Next, remove the cabin air filter and plastic covers above the firewall in the engine bay.
• Working under the A/C condenser pipes, disconnect the coolant hoses from the heater core connections very carefully to prevent damage to the core. Have a jug or pan ready to catch any trapped coolant. The top hose is connected with a powerful spring-clamp and the bottom hose with a quick-connect fitting:
  1. Silicone lubricating spray is rubber-safe and can help release these connections.
  2. Use pliers to squeeze the ends of the hose clamp together so that the clamp opens up, then slide the clamp away and twist the hose to loosen it and pull it off.
  3. On the quick-connect fitting, pull the wire latch open with a pick tool or screwdriver, then wiggle and slide the quick-connect fitting straight off without twisting.

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• Connect a length of rubber hose to both of the core connections. I shoved some cheap 3/8” ID rubber fuel hose all the way inside each connection to create a low-pressure seal.
• Next, soak, or preferably, CIRCULATE the solutions listed below to dissolve and break up the substances that are blocking the core. I ran my hoses into a deep jug with a low-pressure pond-pump inside. I filled the jug with each of the solutions and pumped through the core in BOTH directions to ensure that the solution thoroughly percolates through the muck inside. The solution simply returns to the jug to be pumped in a continuous loop.
• If the flow rate is just a trickle, give it some time, but you can also close your fist over one of the hoses and blow into it to help dislodge blockages, or at least to blow bubbles that will agitate the solution inside. However, do not pressurize with water or compressed air until later.
• During the process, check for leaks inside the car in case the core has indeed become damaged or corroded.

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1. First, circulate an alkali/degreaser through the core at low pressure to remove oil and grease that can bind with scale to block core capillaries. I started with SuperClean degreaser mixed 50/50 with COLD water for 15 minutes in each direction, then switched to Baking Soda diluted in HOT water for a couple of hours in each direction. The color may run dark at first, but it will begin to clear.
2. Next, circulate pure vinegar (5-10% concentration) through the core at low pressure to etch away corrosion and scale for a couple of hours in each direction.
3. Now use a garden hose with a flow-control nozzle to SLOWLY and progressively increase the flow rate and pressure until the core is flowing freely in both directions. This will blow out any solids that have sunk into the bottom of the core. A handful of blackened scale (like sand) burst out of mine, and the flow rate increased dramatically.
4. Circulate fresh vinegar for an hour or so to treat capillaries that may have been blocked previously.
5. Circulate dish soap and baking soda in HOT water for a few minutes in each direction to clean the core and neutralize every trace of acid.
6. Blow out the core and immediately fill and rinse it with fresh coolant to prevent flash-oxidation inside the core.

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• Reconnect the coolant hoses and refill the system with fresh coolant using the process outlined below.
• Do NOT use the incorrect type of coolant! It can react with the components in this system and cause corrosion and clogging all over again. Use fresh blue BMW coolant.
• The E9x cooling system takes just under 2 gallons of coolant. One gallon of concentrated blue BMW antifreeze, when mixed 50/50 with distilled water as directed by BMW, will fill the empty cooling system with a little to spare.
• Remove the fill cap and bleed screw from the expansion tank, fill the tank until coolant emerges from the bleed hole with no bubbles, then tighten the bleed screw carefully and begin the automated bleeding process as follows:
  1. To avoid depleting the battery, connect a 10A battery charger to the jump start terminals in the engine compartment.
  2. Turn on the ignition without touching the brake or clutch (so the engine doesn't start).
  3. Crank the heaters to max.
  4. Set the blower to the lowest speed.
  5. Press the gas/accelerator pedal to the floor for 10 seconds.
  6. The electric water pump will begin cycling on and off for 12 minutes.
  7. Once the bleeding process is complete, check the coolant level and top up if necessary.
• NOTE: Opening or closing a car door may interrupt the process by shutting off the ignition. Simply check that the battery charger is properly connected and restart the procedure by turning on the ignition (without starting the engine) and holding down the gas pedal again.
• When complete, start the engine to check for leaks and test the heater as the engine reaches operating temperature.

[Reverend_Wrong]

While I haven't attempted this yet (and my motivation is diminishing as the weather warms), I really appreciate the detailed write up.

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Originally Posted by Reverend_Wrong

While I haven't attempted this yet (and my motivation is diminishing as the weather warms), I really appreciate the detailed write up.

LOL! I know the feeling! I had reached the point of wearing arctic permafrost protection while driving. I managed just fine, but my passengers had to be extracted from the car with de-icer to separate them from their seats. Thankfully, by the time they had recovered, I was FAR away.

You're welcome. I hope the flush goes well for you!