Your situation and stated preference seems to be perfect match for an EL84/7189 based amplifier. 10--20wpc, small footprint and does not generate a lot heat. I sympathize with your situation. I use a Triode TRV845 PSE / 845 SET amp. I can literally see waves of heat coming from the amp during warmer months !
I would look for a vintage restored amplifier. Dynaco ST35 is a well regarded model. Also Eico HF14 pr, HF86 stereo. Fisher 20a or 30a pr, or SA100 stereo. Heathkit UA 1/2 pr or AA111 stereo. Make sure the amps are rebuilt from top to bottom using new close tolerance components.
If you prefer new, look for a Luxman or Leben amp / both companies offer EL84 based designs that sound wonderful.
If EL84 amps are not appealing then there is a whole world of choices using 6L6GC/KT66 or EL34 tubes. More power, but slightly more heat....however not as much as your 845 SET. The venerable ST70 dissipates a lot of heat in stock/rebuilt condition ! I would consider a new version or an original with new PS and audio circuits that run much cooler.
A slightly more expensive option would be a McIntosh MC225. This amplifier uses a quad of 7591 tubes for a about 25-30wpc of sublime sound. However cost may be higher than your budget.
Good to have choices !