The biggest heat problem i have will be my pinball machine. There are so many lights under the playfield and in the ones ive done in the past it gets quite warm in there but i dont think its enough to harm anything.
If you are worried about heat, get the industrial version. The 16F877A for example will handle 85C. Check the end of the data sheet for the PIC you plan to use.

And like Alain, design carefully.