As long as you apply the same power level, I would doubt you could detect a difference in the temperature profile. Actually, I doubt you could detect the profile just running it one way or the other. The film is not very thick, even for a thick film part. It would seem like if you ran some sort of extensive life test, you could maybe detect a difference in how you drive it. I guess if the part is going to break down at the peak voltage, we could also see some improvement using DC. A good study for your PHD but I don't see any practical use in this case. I would be far more concerned with how effective the heatsink is and want some general idea of the temperature.
Too bad about the parts. If you decide to buy some and run the test, please post the results.