recommendations for amplifiers that don't emit tons of heat

Tripg ,
Buying used saves money if you're going to sell it later . If you can audition the 250 Watt Gilmore Audio Raven stereo class D amp at $1750 new , you may want to keep them . I bought his mono block Raptors with identical specs , save power , and these are as fine as the best I know .They are special and work with all music and should drive any speaker, including Magnepans very well . I've used passive volume control and now a tube preamp and either works well .. They run cool to the touch always and are heavy, although only 12 inches square . Mark Gilmore is a joy to deal with . My two cents' worth , since you asked .. 
 Joe

@don_c55 SST is still alive and well thanks to Wyred 4 Sound.

The original ’Son’ is now the Mk2 version. It runs warm, but not hot. Excellent amp, and phenomenal for the money.

(Spread Spectrum Technologies Son of Ampzilla Mk2)

RIP JB.

I had a similar dilemma a year or so ago.  I have a Pass Aleph 4 (100W/channel) that sounds great but is also a great space heater. Was looking for a suitable "summer" amp that didn't compromise on sound.  I auditioned quite a number of Class D and Class A/B amps and others, including many, if not most, of those mentioned above.  Ended up stumbling upon a used Linn Akurate 4200 at a good price, 4 channels w/200W each into 4 ohms.  Though I wasn't looking to bi-amp my speakers, that's what I ended up doing.  Sounds much better than all the alternatives I heard by some margin.  Runs cool, doesn't idle at 500W, and takes up little space.  My electric and air-conditioning bills dropped substantially, and the air-conditioner can now keep up when I listen to music even on the hottest days. Something about the pitch and tunefulness that just sounds right. Violins and sopranos don't have that edge that I hear so often even on many very high priced tube and solid state amps.  Linn doesn't seem to have much of a presence here in the U.S. where size, power specs, and "slam" matters so much and seems to impress many listeners.  Linn's focus seems concentrated on Europe where listening spaces seem to be smaller and more intimate.  I listen to quite a wide variety of music including a lot of classical music. I don't think Linn gets its due.

I also run 2 linn 4200 amps into a pair of Pioneer S-2EX (TAD) speakers.
Depending on how your speakers are wired, biamping ( sending the 
signal twice, once to the tweeter and the other to the bass) will allow 
more power to reach the bass drivers.  The Linn amps have an amazing
ability to render the musical sound stage.  I've compared them to Bel Canto 500s and was disappointed by the BC 500's lack of
dynamics and flat soundstage,
so all digital amps are not the same.  I also use a pair 
of Linn 5105 in a bedroom about the same size as your current room
and the Linn sound staging, bass, and speed are also there,
The Linn 5105 is an affordable stereo amp you might want to look at.
The Linn amps have signal sensing so they will power up or down seamlessly. I guess I'm a linnie when it comes to their amps. 

Karan KA-I 180Mk2

2x180W/8 sliding bias , cold like a stone ...second hand, almost new like ex demo  in TX about 5.000 $