I have pesonal experience with hotplates.....
I have run them off and on since the 80's. (back when they were great equipment.) and will agree that they get pretty damn hot, more so than any other brand I have had experience with.
My current 4 channel used to shut off within 15 minutes of high volume listening. I tried a couple of different mounting locations with no luck.
after the I did the last update two years ago, I have had zero problems with heat.
They need some type of air movement across them. I am using a pair of 3 inch brushless fans on the 4 channel in an enclosed rack, and can now play till the batteries run down.
MAybe I need to switch to 6 volt batteries to add more playing time?