recommendations for amplifiers that don't emit tons of heat

No mention of price point above.
I have the latest Spread Spectrum Son of Ampzilla MK-2,and I could not be happier It runs in pure class A to 10wpc then class AB .up to 220wpc into 8ohms,
340wpc into 4ohms and throws off very minimal heat. Class leading performance 
And compact in size. $4200 retail.

Regarding larger amplifiers my Son of Ampzilla mk2
Is very fast. The late great James Borngiano was a great designer.
This amp has a Huge 2,000va transformer for control and I believe 12 bipolor
Transistors per channel and over 100k in capacitance.  And grounding eliminates ground loops in this amp low level detail is very good also.
The matching preamp is very good also ,but I have a custom Lundahl transformer based 4P1L - DHT preamplifier Which being single ended really pulls the music out. TIP OF THE DAY - Buy Stabilant22  to put on all Audio connections just one mating side very thin coat,first clear everything with Isopropyl Alcohol 99%
If possible.lasts for years and by far the most technologically advanced on the market . If it's good enough for NASA,then I am good with it also. I use on tube pins and everything else give it a solid 30 minutes to dry, great stuff !!