I've been developing C-41, E-6; EP-2, RA 4 and a little P30 and R3/3000 for, lo, these many moons now.
A couple of observations:
I've screwed up and developed in C-41 chemistry at 35 degrees Celsius, instead of the required 38 degrees. That is 3.0 degrees lower than is should be, for the same time, 3 minutes 15 seconds. I print my own color, and I haven't noticed ANY unusual color correction necessary with these negatives. I would suggest that temperature control is NOT as critical as the "everybody knows" perception.
I've made a similar error with RA-4 going the other way; 3 degrees too hot - with the same results.
The time of 3 minutes 15 seconds ... It will take some three - four (?) seconds to fill the tank in the processor, but it will take about the same amount of time to empty it .... so the net effect on time will be near nothing. Again, I don't think the process is sensitive enough to be worth agonizing over it.