I wouldnt bother with an intercooler on the stg 1 set up, the blower is barely working hard at that point and the intake charge is only 20-30*F over ambient from what I’ve seen.
depends on how hard you push the turbos and how well they are matched to the motor… I believe the goal of the turbo car is monster power (with the built motor and all) so the turbos will probably be pushed pretty hard, so in that case an intercooler would be a good idea… but concievably you could aim for a lower power goal, dial back the turbos and run a low boost set up with no intercooler. As long as the compressor spends a good portion of the power band in a high efficiency island it shouldnt make a massive amount of heat.