recommendations for amplifiers that don't emit tons of heat

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 $

Ie: McCormack DNA amps-

They run cool when at normal house volume. Only very slightly warm to the touch %99 of the time.

 Any descent SS amp would be good,... A/B is recommended.
How about a used Sunfire 300 - not too heavy, reliable, sound amazing, and run very cool to the touch. used ones are about 500-800 for the 300 W model.

300@8 / 600@4 / 1200@2, /  stable to 1 Ohm

I decided to give class D a shot and purchased the Audio Research DS450. It is the best sounding amp that I've heard in my system. My friend and I have compared it to 4 other amps, including a Pass class A design, and it has come out on top every time. The closest competitor was another class D amp, the Hypex NC400 amps. They are available as a kit for around $ 1,500.00.

Primare A34.2 or A60, which has a DAC.
http://www.primare.net/product-list.asp?m=1

I'd surely place these on my must-demo list; but I don't think you'll find any used A6s yet.