The cheese is just coming from being scalded, milled, formed, etc., and the curds are still warm. You'd like to keep them at that same warm temperature while they bond/knit in the press. We're not talking about excessive heating. The idea is to not let them get chilled to the point that they are resistant to getting neighborly. I try to move quickly when transferring the curds from draining, to milling, to forming, to pressing. Even Cheddar cheese varieties stay warm while cheddaring and milling.
I've kept mine warm while pressing lightly under whey. I have also pressed from light to heavy pressure in the pot (whey removed) and that pot sits in a double-boiler with warm water surrounding the pot with the cheese. It doesn't overheat. I monitor the temp with a wireless humidistat so I don't overshoot and I monitor pH level during the press so I don't undershoot. A clean towel over the pot helps to hold in the heat.
As for what cheese styles benefit from keeping the curds warm while pressing? Seems like all pressed cheeses would be in that category because they all want to have nicely knit curds.