Hi everyone, long time reader, first time poster.
Back on topic, the "heart" of all electronics in all F1 cars is
TAG-310B (PDF File). (not sure if they use 310B, 210 or 400 module)
As McLaren state, its power consumption when operational is about 40W (~14Vdc/~3Adc) and the internal temperature should not increase 70 deg C. It is not an easy task to accomplish this even it is not heated by other car internals, its cooling is obligatory.
The MPU they use, i believe, is
PowerPC 476FP, and for the tasks it is designed, is better than any PC-processor (they are different though). As I can see, they use some weird method for programming - "Application code is autocoded using our Graphical Development Environment (GDE) from Matlab/Simulink control modules." - this adds some overhead for both code and time (this means a directly programmed less powerful MPU should be capable of doing exactly the same work), but the benefit of using their system is that they can change the firmware very fast without the need of highly experienced software developers with thorough knowledge in engine and transmission control.
But there are other electronic units that require cooling (well, may be not all of them), for example ingnition and injection modules:
IGN310 and
INJ310
In general, electronic components are divided into temperature grades, with general purpose grade 0-70 deg C (rarely used), industrial grade (-20 to 105/125 deg C - lower and upper limits vary upon manufacturer and part), and military grade (-40/60 to +150/+175 - again vary upon manufacturer and part). I doubt if they use anything else than military grade components. Any decent electronic device should be capable of working at 100 deg C, but keep in mind, that the crystal temperature of every heatsink-mounted semiconductor is at least 5 to 20 deg C (and may be more, depending on the design) more than the temperature that you can measure on the heatsink surface.