Interesting that the low end of this phase transition range coincides with the maximum safe temperature for mammals and birds. It could be that the delicate biological mechanisms we've developed over the years are highly sensitive to some of the bulk characteristics that change in this range.
The paper talks about this. It's not just mammals and birds, proteins in general become less stable over 60C:
"This raises the question of whether temperature-driven structural changes in water affect biological macromolecules in aqueous solutions and in particular in proteins... It was found that the temperature stability range of the protein is confined to the reversible interval 45–65°C. ... In all cases the critical temperature of the protein denaturation is very close to the crossover temperature T* observed in all the properties of liquid water reviewed in this work."
This is probably why sous vide temperature is around 60C.
Although highly applicable you have to remember evolution is a thing. Proteins where there are no selective pressure to operate at high temperature are likely optimal in the ranges in that state of water. Hyperthermophiles live at 80degC and above only, they're still made of proteins. Their protein structures are highly similar to other organisms found at lower temperatures, but with modifications such as additional disulphide bonds that increases stability at high temperature. Most of these thermophilic enzymes operate very inefficiently at cooler temperatures or not at all. We already have that sort of broad insight from just looking over evolution and ecological niche.
The more interesting thing this finding has to offer is just understanding at a finer detail how proteins interact with water at all, and if there are any properties specific to each state. There might even be cool things like proteins that switch function given the water phase transition. You might find this sort of thing in chaperones related to heat shock for example.
I wouldn't use 'probably' at all. The level of proof submitted is incredibly light - it only inspects two and a half proteins - and doesn't attempt to inspect the relationship between its proposed mechanism (change in hydration shell density) and protein denaturation.
They show two graphs of protein denaturation curves showing maximum rate change in 50-65 degree range, and a curve of a different protein's hydration shell density changing. At the very least, showing correspondence between hydration shell density and denature curves within a single protein would be significantly more convincing.
While protein folding and interaction is devilishy tricky to compute, the basic idea that injecting extra energy into a system thats held together only by weak hydrogen bonds will disrupt structure and function hardly requires invocation of additional forms of water.
This isn't to say that the claims may not be true. But I would not jump to "probably".
In fact, your quoted statement doesn't even say that proteins become less stable, what the quoted statement says is that a SINGLE protein (lysozyme) undergoes irreversible structural changes over 65 degrees.
We know of a variety of high temperature resistant proteins (Taq Polymerase for example). While is certainly true that most "ordinary" (ie non extremopile) proteins will probably suffer irreversible structural changes in about that temperature change, it's not super great proof.
Thats because you have enough thermal mass and evaporative cooling capacity to withstand those temperatures for a short period of time - ie, very little of your body will experience drastically elevated temperatures for long - if at all. Remember that air (even humid air) is not a super great heat conductor - so while the air might be very hot, it's going to be pretty bad transferring that into your body, which in turn has a lot of mass to distrube heat over, and good conductivity to move heat away from contact areas. And that whole sweat thing works pretty well too (especially in a dry sauna).
Being submerged into a 90 degree water bath will probably rapidly hideously wound you and/or kill you.
