Explain Amp classes & how effects sound?

I see class A, B, AB, Class T, etc on amplifier specifications. Can someone explain (simple terms) how each class (even class T) effects sound quality?
Thanks...so a class T amp would run cooloer than a Class A, thus a smaller chassis. I get it
In terms of heat:

class A => hottest but otherwise the most linear/lowest distortion

class A2 (tubes only) grid current may flow in the tubes during part of the waveform but the tube is conducting through the entire wave cycle. This allows for more power but has greater requirements of the driver circuit.

class AB => less heat, slightly more power but slightly more distortion

class AB2 => (tubes only) similar idea to A2, but the tubes stop conducting through part of the waveform. You get a lot of power and a lot less heat, but crossover distortion is more pronounced.

Class C => not applicable to audio

Class D => so far, for practical applications so far is transistor only. The devices are either fully on or fully off, avoiding the much greater power requirements of operating the transistors in the linear region. This makes the most power with the least amount of heat. Distortion can be very high, but this is a developing field, and is likely the area with the most potential for improvement in the next ten years.
And in follow up to Atmasphere post, Class D is the class T amp the OP is referring to.
What about class H. Soundcraftsman had some amps in the 80's class H. I had one and ran it HARD! Never got more than just a tad warm! I guess the design never took off.
Also class D had NOTHING to do wit digital. Many people presume wrongly that the D stands for digital. This is just not true.

There are amps being sold as class A but in truth some of these are Class AB with a high class A bias. But how much watt do you really need? I just spoke with someone who ones 1000watt mono amps. He never saw the needles move beyond 15 watt and normally not beyong 5 to 10 watt.