pbonsalb wrote Longboarder made some good comments about supercharged E9x M3. The most popular and affordable kits use a water to air intercooler with a small coolant capacity that can't keep up with sustained use such as on a track. People have gotten around that with larger trunk mount tanks. There are also refrigerant kits that use the car AC but I am not sure anyone has tried one on an E9x M3. Evolve, GPower and AA made or still make centrifugal systems with air to air intercoolers that would probably be better but those systems cost more.
I can only speak for the G-Power (GP-Infinitas) system.
It can get
VERY warm in the summer where I live here in Northern California, like 109f a couple of weeks ago.
I've had my car to Thunderhill Raceway on a 103f day as well.
The car doesn't suffer noticeable (to me) power loss in either situation, but on track some fluid temps will eventually climb high enough to put the car in limp mode.
( I think the GP-Infinitas kit is priced much lower now, than it was when my kit was purchased in 2009)