[dparm]

38psi hot does seem high given your cold/starting PSI. Makes me think you're putting too much heat into the tires, which would make sense if you're getting understeer and the instructor is telling you to improve your turn-in.

Full disclosure, I haven't had an M3 on track in over 2 years now so I can't remember exactly what mine used to do, but I don't remember ever seeing as high as 38 on the 255/275 setup.