I used to hot laminate Epson Premium Photo Gloss paper when I was doing commercial printing some 10 years ago, with no ill effects providing the inks had cured properly and the temperature was correctly set - the paper is in the nip of the rollers for such a short period that the heat doesn't adversely affect it. I still have a few images on the wall here, printed on Epson PGPP(250), hot laminated and mounted on Foamalux board, and they're still absolutely fine after that time.
The major difference between cold and hot laminating films is that the latter are (or were) usually considerably cheaper - I'm not aware of any significant differences in the performance or longevity otherwise.
Even with cold-laminating films, some degree of heat-assist, i.e. a low temperature setting on the top roller, is always recommended and helpful in getting good adhesion and avoiding potential silvering.
I have to say, though, that I was very happy when I was able to give up laminating entirely - it was always a necessary evil, and one part of the process that I never enjoyed.
Regards,
Malcolm