Overheating has nothing to do with the soldering - soldering is necessary when the components pop off the board due to the brittle solder, yielding one red light and an error message or the three red lights.
OP, you can try dusting it with an air duster externally, but I really recommend cracking the thing open. It'll take you maybe five minutes if you've never done it before, and all of thirty seconds if you order the tool to pop out the rear tabs. You'll also need a Torx 10 screwdriver to detach the top of the case from the metal chassis. It's all pretty simple.
That being said, if you're going to do all that, you might as well do it properly. Use a Torx 8 screwdriver as well and remove the x-clamps. Clean the CPU and GPU off with 95% or higher isopropyl alcohol. Apply an appropriate amount of replacement thermal compound (Arctic Ceramique is easy to use and non-conductive, good paste to learn with) onto the dies, then mount the heatsinks back with a replacement bolt and washer setup. It's about a thirty minute job start to finish and will drastically drop the temperatures on both the CPU and GPU while greatly reducing the chances of the three red lights occurring in the future.
It's seriously quite easy and far more of a mechanical job than an electrical job - just disassembly and reassembly, no technical skills required.
EDIT: Just saw the comment about running the system with the top off. In my experience with one of my Xenon consoles, the system actually runs hotter with the case open. I guess the air doesn't dissipate as effectively.
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