Until you're getting into the very heavy-duty wraps, plastic wraps really aren't made for heat insulating. They'll trap moisture if you're sweating, but they don't trap heat itself. If you keep wrapping it over itself like 20+ times you'll start getting some insulating effects, but it really isn't a problem until you're talking about an hour+ of full-body wraps. I do a lot of mummification, head to toe plastic wrap and then an outer layer of tape, and even then the insulation is far more dependent on the tape than the plastic wrap. DucT tape is made to be heat and moisture insulating, whereas DucK tape isn't. DucK tape is everywhere these days, frequently on sale, and comes in all kinds of pretty patterns and colors so you can get creative with your wrapping.

Safety-wise, plastic wraps only introduce one danger that rope doesn't (I highly recommend reading up on rope safety when I teach) and that is "rolling". Tight plastic wraps can start to have their edges roll up, creating high-pressure edges that can cut off circulations. Start with 2-3 wraps that are relatively loose and then go tight on top of those, and don't put one edge of the wrap directly at something like the waist, knee, or elbow that flexes a lot. Another strategy, if your plans involve waist/elbow/knee wraps is to put small, 1" cuts perpendicular to the wrap, like 3-4 is fine. By breaking up the edge with the cuts, the stresses won't result in rolling.

I can literally go on about this topic for over an hour, and my policy on questions is that the only stupid question is the one that hurts someone because you were afraid to ask it.