Power supplies tend to have higher efficiency at the higher voltage, this is a known fact, google it...
I don't have to google such basic/common electrical theory, and if I do I would be very careful about the source. You are correct about that being a known fact. Just keep in mind that the difference on the "Primary" side of the transformer only will not give you much of a difference especially when you are talking about the heat dissipated by the AVR, not your cabling system. The fact is, the secondary side of your amp (the so call rail voltage) remains at the same voltage, your selector changes the transformers turns ratio so the secondary voltage remains the same, hence the same load current. The only cooler part is the primary side of the transformer core and windings, hence I concluded why the difference would be slight.
Reasonably well designed power transformers are very efficient, relative to things like motors class AB amplifiers. You can also google for the related "known facts" in that regard. When I say very efficient I mean in the mid to high 90's percentage wise. So the difference between a 220 to say 70V vs 120 to 70V in terms of efficiency is probably less than a couple of percentage point, if that.. When listening to music the power consumption is probably less than 200W average most of the time. Of that, the transformer would probably account for about <5 Watts in losses with the remaining losses in the electronics so double the primary voltage/halving the current would probably save you a watt or 2 in terms of heat dissiption. all these are just in order of magnitude, not meant to be accurate.
I don't doubt your AVR is running cooler, but either there is something else at play we do not know about, or your definition of much cooler is not the same as mine or others.
I read an article about 3 months ago, on why they are going to be raising the voltage and lowering the amps they fed led lights, because a set of tests showed doing so multiplied the led's life over 80%...
That can be true for LED
Same thing with power supplies, When building my work comp. system Iused to have a 120v 60a and when we built the new building I went to a 240v 30a. Now I know in this case a lot changed, new equipment {but more of it} in a different room {but a smaller tighter room}... But my old stack used to be in a 10X8 room full of office supplies and when the comp was running, you couldnt stand in there it was like a 100K btu heater, we used to put a fan in the door in the winter to scavenge the heat, now the new system is in its own non vented closet {very small} and its never HOT, warm, but not like the old system..
Yes, if you are comparing a drawing of 30A vs 60A that is significant in terms of total heat dissipation but your AVR does not draw rated amp, should be no where near on average basis.