Heat is energy and it will have some impact on the longevity of the print. I am not aware of any extensive test, but is almost a consensus that a few minutes of higher temperatures may cost you some years on longevity.
While it may be a consensus (shown through testing) that higher temperature over long term is detrimental to color prints (both chromogenic and inkjet), I'm not sure this applies to a minute or so in a heat press at 130-180 degress - I just can't imagine this would cost years of longevity in regards to the fade characteristics of the dyes - or any significant period of time for that matter. This would mean the heat would have to create some substantial degradation in the dye characteristics of the ink which could be tested and seen pretty easily and I"ve never seen any evidence like this. But one reason heat is detrimental is it accelerates the process of other image degrading processes such as humidity, gases, UV. I think this is a case of logical or cirumstantial thinking, but without any real basis. Dry mounting has a long track record (it's been around for over a century), much longer than any current color print process.
Usually when mounting and archivability is discussed the concerns are more about the inability to remove the print from the mounting material (which technically makes in "non" archival by some), the adhesive and mount board used in the process, and the durablity of the adhesion between the two surfaces. Additionally with any mounting of inkjet prints that have been printed from rolls, the mounting process can stress the receptor coating and make it crack. Of course somehow the print has to be flattened, and maybe dry mounting may be better than reverse curling.
Cold mounting removes the heat part of the equation , but there is some question that adhesion qualities between the two surfaces is subject to failing more than most dry mounting techniques. That doesn't make it bad, it also has a long track record and using proper materials certainly makes it worth considering.
Avoiding any type of mounting for those trying to offer museum archivability would make sense, but then the print would need to be cared for with the same attention that a museum offers. That's probably not going to happen unless it is owned by a museum, and as much as we wring our hands about fading issues, fading is one of the least likely reason a print will die over time.