Hello,Yes that makes sense, as long as your realize that the hotter unit actually generates less heat.
Yes, class D amps use power much more efficiently. And if you don't cram class D amp modules into the smallest possible cases with no or little ventilation, they run pretty cool.
Personally I use a quite large case for my modules so that there is lot of room to keep things and wiring separate to minimize any possible interaction by RF or magnetic coupling as well as to keep things as cool as possible. I even us thermal coupling compound on the amp modules so that they are getting as much heat transferred into the chassis as possible. (Not necessary.) I have worked in the medical electronics field for over 40 years and firmly believe well designed equipment that runs cooler lasts longer. So I may overdo the cooling, but this is DIY and I do it because I want to.
IMHO this extra cooling and spacing between components costs not a lot and is well worth it.
Regards,
Greg