If you're just drag racing a few runs in the evening or running around on the street in a moderate climate, you can run without an OC just fine. Since winter is coming, you can tune now, make sure you have a good running engine (plugs, coils, injectors, fuel pumps, all in good condition), then when spring rolls around, install the oil cooler. 260F is not great, but not the end of the world or your engine. Run a high quality synthetic and you'll be fine.
If you are going to a road course without an OC, I'd say you're crazy.
E92 335i/6MT Dinan Stage 3: intercooler, oil cooler, intake, flash, exhaust, LW dual-mass flywheel.
Vishnu PWM methanol custom trunk mount, Diffsonline 3-clutch Salisbury custom diff, Ohlins Road and Track coilovers, Vorshlag camber plates, much more...
E28 M5 w/ buncha stuff, R171 SLK350