What are the effects of enzyme exposure to high temperatures?
The answer is that it completely depends on what specific enzyme you're talking about; some of them will and some of them won't. What you wrote is correct, that increasing temperature of most enzymes (although there are exceptions) will increase their activity to a certain point, after which the proteins lose their 3D structure and become unfolded.

Upon cooling, it all depends on whether the enzyme can re-fold by itself or not. Some proteins when heated form aggregates, which are more stable than the original conformation, and so generally won't refold with cooling. Some proteins are able to fold into proper conformation by themselves, while other require assistance from chaperone proteins in order to fold correctly. Many of these chaperones are called heat-shock proteins, which are upregulated in response to thermal stress. That points to the fact that many proteins can't just refold on their own, and require help to regain their original conformation from these HSPs. 

So the real answer is that it all depends on the specific protein. It also depends on how much you heat the enzyme, and how much of its 3D structure you affect, if you only partially denature an enzyme, it's more likely to refold than one that's been completely denatured. However, if you want an answer about enzymes in general, I'd say that most enzymes after denaturation aren't able to refold properly and regain their enzymatic activity, so the damage is permanent.