It depends........An original Shaker bubble is made from a RIM plastic material (Reaction Injection Molded). It is comprised of a base 2 componant resin which cures under heat and pressure in the molding process, this material is filled heavily with talc to give it stability and temperature resistance. This material was engineered specifically for automotive under hood environments, heat and chemical resistant, etc. Normal engine opperating temperatures are not going to affect it, heck I've even seen them survive short duration carb fires with no apparent damage!
Now.......Aftermarket bubbles sold today. They are made of fiberglass. NONE of them are made in the RIM process (cost prohibitive tooling, etc.). Fiberglass is pretty decent for automotive use, engine heat won't affect it much in normal use, but you could have problems if it were to get in contact with open flame, it burns/melts pretty easily, especially if coated with gasoline like from a burping carb fire, etc..
I don't know if this answers your question but it might offer some explaination of the materials involved. In my experience the original bubbles seem to stay realatively cool in opperation, the original material does not hold heat very well. Even though its heated from below (radiant engine heat) it's also cooled from moving air above to counter it.