I had overheating-related problems with my DCT on the Sebring club course last year. About 15 minutes into a session the DCT would begin short-shifting at about 5k, and shifts would become sluggish. Ambient temperature was in the 90s (does the car's thermometer top out at 86?), and my oil temp reached 280.
A couple months later on the Sebring full course (this includes the back and home straights) I didn't have as much of an issue. Those straights were long enough to give my engine and DCT a chance to breathe, though the car sometimes acted up around turns 14-16. I still hit around 270 oil, but I had no immediate problems (just nasty oil next time I went to change it, of course).
I had the BMS Stage 1 for both sessions, so the increased boost no doubt exacerbated the problem.
Neither time did I get any engine or DCT heat warnings, so the upshot is the car won't tell you it's starting to limp from heat. It'll recover once it cools down though. I've already ordered an ETS intercooler and installed the BMS oil not-a-thermostat, so we'll see if those help out. The not-a-thermostat, btw, dropped my temps to 210-220 daily from 230-240 (the factory thermostat is set to 110C/230F if someone doesn't already know, which is etched on the thermostat).