Why warm amps sound better.

Yup, sunfire is a/b. Doesn't it switch to class H ?
Downconverter goes into class h?

That's right, Sunfire is class A/B. The Carver amps were class G.
I leave my Sunfire turned on 24/7. The sound from the amp at idle for a few hours is clearly better than after a cold-start.

I turn my primary system on about 1 hour prior to a listening session. All electronic parts need to reach thermal equilibrium to operate at proper spec. I believe this to be true even for speaker cones.   

In addition to bias points (operating points) filter caps need to charge up and they charge on an exponential curve. So that last nth degree takes a while. Filter caps are usually electrolytic and electrolytics are funny things, sort of a cross between a real capacitor and a battery (more on the cap side of things though). They are also used as coupling caps in solid state gear and for that reason need some time.

Transistors have a non-linear capacitive element that is inherent in their junctions (which affects the kind of distortion they make). This aspect is affected by heat and voltage (most radios these days are tuned by varactor diodes that take advantage of this effect). That quality of the devices has to stabilize and if the designer did his homework, that happens after a period of time rather than just after the amp is turned on.

IME solid state gear really needs to be on all the time to sound its best, though I have run into to some pieces that actually sounded worse after a day or so.

One might ask why such tiny effects might be so audible and the answer is that it has to do with distortion, and tiny amounts of it at that. But the distortion involved happens to be of a kind to which the ear is actually more sensitive than most test equipment, which is to say that we can measure that the distortion is there in trace amounts but to the ear its pretty obvious. This is because the ear/brain system uses the harmonics that are affected by this distortion (5th harmonic and above) in order to figure out how loud a sound is. So the ear brain system has to be pretty sensitive to do that as our range of hearing is pretty wide from soft to loud.

This is why the tube/transistor thing has been going on for so long BTW. Tubes inherently make less of these higher orders than transistors, which is why they sound smoother.

To add my 2 cents. When I was a kid we left my friend’s Fender Champ guitar amp in the trunk of my hot car for a few hours.

when we plugged it in it sounded better than it ever had.

The BHK 300 amps (dealer alert) have a solid state section meant to stay on all the time and the tube input section is what gets turned on when the front power switch is engaged.

i have even noticed it takes my strain guage phono cart takes some time to warm up and sound better.

Much to what many people believe, SS amps require more warming up than tube amps.  Some SS amps require 2-3 days to yield their full potential.  Additionally,, many amps are never afforded the opportunity to fully break in when purchased new.   First let your system settle in for no less than 1000 hours, then use the mini break in for a few days and never let your system lay idle for over week.  Breaking in is vitally important for your system to find its least resistant grounding path and, believe it or not, this takes lots of time.  When burning in your system, it is not necessary to play music loudly with heavy rock.  Simple classical music at low levels is sufficient but continuous pink noise also works magically.  Play nothing at all and just leave your sytem on to let your grounding system establish itself.  Grounding is something many audiophiles miss or not pay enough attention to robbing and limiting the full potential of one's system.