Too many variables. If it's too hot for you to keep your finger/hand on, it's too hot for your pet. :wink:
What kind of plastic? Depending, I might be more concerned about potential off-gassing with some plastics being heated up.
Monitoring temperatures is important, so it's good you're thinking about that. Do you have a
temp gun? IME, they're the best (not only) way to measure basking surface (and
bath water) temperatures.
You can also monitor how hot the branch is getting with a digital thermometer w/ probe. For most accurate results, I think I'd tape the probe to the hottest part of the branch.