I’ve been using a tacky tack pad (one of the ones that has no blanket or felt over it, just the foam over the mesh/waffle stuff) for several years-no problems, the horse that always has a nice sweat pattern always has a nice sweat pattern, the horse that often has a not so nice sweat pattern has a not so bad sweat pattern. I also use wool felt and sheepskin and generic cotton English pads depending on my mood and the weather and the saddle I’m riding that day.
I havent noticed any problems for the horse using it. I have a similar English AP shaped pad that I seldom used because the straps on it were annoying, not to mention superfluous, so I cut them off. Those suckers do not slip or travel around, so why the heck put straps on it?
It is a great convenience being able to hose the thing off, too. Longest rides taken with this type of pad has been, I dont know, fifteen miles or so, maybe? Since I live in the Deep South and routinely ride in temperatures around a hundred and heat indices higher than that, I would expect that if they could cause significant heat buildup that my horses would have blistered backs. They dont.