Sounds like you could do with a program to trigger a hair dryer, or perhaps, a fan heater. Or perhaps just a shunt to switch said fan heater to blow into the booth.
I’d go to your local university and suggest it to the electronics department as a project. The Electronics students in my dorm were always building this sort of thing.
As for synching it up to video, you’d probably be best looking at flash video. Make the movie in After effects, export it into Flash and use actions to trigger this other program (that the electronics students would have put together). It’ll still take some guess work for the timing, but all should be possible.
Alternatively, you could pay a kid to stand there all day and switch on the heater on cue 🙂
Actually, just found this: https://www.pontech.com/products/sv200/
It’s a PC controlled servo. So you could have your fan heater running, have Flash activate the program, which throws the switch, which redirects the air flow into the booth and then switches the air back.
Graham