I've had overheating problems every time I went to the track with temperatures in the mid-90s and up. I've had both engine oil overheating and DCT overheating issues.
Symptoms of the DCT overheating are:
* slower than usual shifting
* not shifting at all
* shifting by itself to higher gears
* loss of lower gears
By the time you get the above symptoms (except slow shifting), you would typically get an overheating warning message.