recommendations for amplifiers that don't emit tons of heat

Your speakers are 92db and nominal 8 ohms and with your small room you don't need that much power. you could getaway with 20-70wpc in a quality class A/B that will not over heat your room. Class D is an option but I would listen to one first see if its your cup of tea.  There is quite a few quality amps in your price range and at the lower watts you can get more for your money as your not buying power.

Those Paradigms like high current/voltage amps like Anthem. Paradigm is the parent company of Anthem. I've heard the two paired and they sound great. 
I wouldn't be afraid to push 200 watts through your speakers. Your going to maintain driver control better than if your easing in to 70-80 watts. You want better braking.

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.

Roksan Caspian M2.

@audioman58
I’m not 100% on what you mean by braking... assuming it’s analogy for greater control over the speakers, that’s my experience too. The power isn’t so I can rock out and anger the neighbors, but the opposite. In my experience, more powerful amplifiers don’t need the volume as high to get a full, convincing sound.

Is there a point where it gets too powerful, and the sound suffers? I’ve read extremely powerful amplifiers can sound sluggish. Not sure what to make of that.

And budget is $2000. I prefer the bang for the buck of buying used... reputation for reliability is important