While I do not have any research for you, I used to teach a kickboxing class that immediately followed a heated yoga class. Since the classes were back to back, there was little time for the temperature to adjust until we were fully into the kickboxing class. It did affect the intensity of my class (I had to make it less intense) as I felt the heat made it unsafe for myself and the participants.
There are problems associated with exercising in the heat, and there were definitely times that I felt nauseated during the class. In addition, I did not recover as quickly as when the temperature was normal from the beginning.
Heated HIIT or kickboxing is not worth the risk, and my question to those who are marketing a class like this is WHY?