I'm running Win7. Whatever the problem is, it should not happen. Playing a video is not a very hardware-heavy thing.
My settings are nearly all maxed with 1920x1080 but capped at 30 fps (else the game will stutter). I can only aim at 60 FPS by toning them down, but I don't want to right now. For my problem this doesn't have any effect anyway. Videos are videos.

How do you know it's not overheating? When I had overheating problems the PC just shut down to protect the hardware. I only found that out by using a monitoring software to watch the temperature.