I recently had to figure out how damping rates influence tire temperature and as i found out, that this was a huge research topic on its own.
Normally my basic approach is to find the optimal tire temperature and make sure that the camber is correct enough to ensure even distribution of heat throughout the carcass. The next thing to do would be to make a couple of runs which ensure that the temperature is reached before heading for a good track testing run.
However, there are a huge number of theoretical data showing that damping actually affects the tire hysteresis and recovery time. I have done no practical testing till now to show any difference in tire temp, but i would like to know the science behind it.