I read in a book that if a protein is heated its 3 and/or 4 structure is denatured but upon cooling the protein will not be able to resume that conformation back. Is that true? I agree that if those bonds are broken there is no guarantee that those bonds can be reformed but wouldn't it depends on the type of protein, its size, and how many competing bonds there are in terms of determining if it can resume this structure?

Some proteins can refold back into their original conformation. The slower that the protein is cooled, the more likely it is that it can return to its original conformation. It varies from protein to protein. Some can never regain their original conformation. Only a fraction of those that are capable of will fully restore.

I recall certain proteins also have "helper" proteins whose interactions help those proteins acquire their proper secondary and/or tertiary structures, so whether those helper proteins are present may also determine if a protein can return to its proper structure.

@OP, Are you talking about breaking disulfide bonds or some other type of bond? Some proteins are capable of reversible denaturation but not all proteins are. Another experimental variable is concentration (this is very important in urea denaturation, but I am not certain about heat denaturation). In vivo molecular chaperones can aid in the refolding process.

I have read that if disulfide bonds are broken they cannot be reformed. However other bonds may be reformed. I take it that there is no general answer to my quest but all varies case by case.

The unfolding and refolding of ribonuclease by adding and then removing urea also included breaking and reforming disulfide bonds. Whether or not they reform with the correct pairings is an interesting part of the Anfinson experiment. One needs an oxidizing agent to reform them from sulfhydryl groups. From what I know you are correct about this being a case-by-case question.