recommendations for amplifiers that don't emit tons of heat

I’m no model “Mr. Green” when it comes to conservation, but I’m astute enough to see when excess goes so far beyond the bounds of tolerable waste that it deserves dishonorable mention. Truly, some vacuum tube power amplifiers merit that distinction. Other forms of conspicuous consumption pale when compared to the staggering inefficiency that you enable when using a stereo power amplifier that features eight (or more) hi-power vacuum tubes in its output stages.

Listed below are basic performance specifications for three closely comparable stereo power amps. One is solid state, the other two are premium vacuum tube power amps. Take a look; compare the data. Also, be assured that what’s shown is entirely representative of equivalent product offered by other makers. The specs are as extracted from the relevant source's website.

(1) Parasound model Halo A23 (solid-state) stereo power amplifier: Continuous full power output = 125 Watts (x2) into 8Ω, 200 Watts (x2) into 4Ω, 20 Hz - 20 kHz, both channels driven.
Total harmonic distortion: < 0.06% at full power output.
Power required: 25 Watts in standby idle, 700 Watts at full power output into 4Ω loads.
Mains fuse (USA): 6.3 Amperes.
Street price: $995. ea. (Audio Advisor, on-line site).

(2) VTL Amplifiers Inc. model ST-150 (tubes) stereo power amplifier: Continuous full power output of 150 Watts/channel is loosely claimed, but conditions of measurement are not specified.
Specified power output = 120 Watts into 5Ω (driving both channels assumed, but not specified).
No power output ratings were provided for 8Ω loads and 4Ω loads.
Total harmonic distortion: < 3.0% at 120 Watts into 5Ω load, 20 Hz - 20 kHz.
Power required: 240 Watts* in standby idle, 800 Watts at “full power” (no conditions given).
Mains fuse (USA): 15 Amperes.
Listed price: $12,295. ea. in Canadian dollars (Melbourne Hi Fi, Victoria, Canada, on-line site).

(3) VAC (Valve Amplification Co.) model Phi 300.1a (tubes) stereo power amplifier: Full power output of 150 Watts claimed, but no conditions specified, so refer distortion measurement (next).
Total harmonic distortion: < 3.0% with 135 Watts/channel continuous avg. power at 1 kHz into a 4Ω load when connected to the 8Ω output tap (stereo mode).
Power required: No power consumption stated. It’s likely slightly > than for VTL ST-150*.
Mains fuse (USA): No info provided.
Listed price: MSRP $22,000. ea. (Scott Walker Audio, on-line site).

*Both tube amps draw more power when in standby mode than a 55 inch Sony LED/LCD TV set does when in use. Note that 240 Watts standby is equivalent to continuously burning four 60 Watt incandescent light bulbs without shedding any usable illumination—just generating lots of heat.

glennewdick---As you say, KT88 filament current is specified as 1.6 Amperes. The related filament voltage is 6.3 Volts. That's TEN WATTS of power dissipation that's consumed merely to "light up" the quiescent KT88 vacuum tube. In that state, the tube is merely at passive idle; it's not doing any functional amplification. It's serving only to emit heat + dim illumination. Additional power is then consumed when the tube is subsequently biased to pass current from cathode to plate. That's truly archaic efficiency.

Yes---and 1.6 A. x 6.3 V. = 10 WATTS.

And that power is consumed merely to "light up" one KT88 to a quiescent state, where it does nothing more than emit 10 watts of heat and light. Additional dissipation, over and above this wasteful filament dissipation, is required to perform active amplification.