Yes the air does heat up, but a point is being missed here. You have to look at the temp delta. If the air is 100 degrees before it is compressed and 160 degrees after the intercooler, then there is a 60 degree delta. If you lower the pre-compressed air temp 20 degrees, than the compressed AIT should be 20 less also (just as long as the intercooler coolant isn't super hot).