When does my class Atoll IN200 A/B integrated switch from class A to class B?

That seems extraordinarily high for an integrated that's rated up to 120W into 8ohms and which has no external heatsinking.  In fact, I find it hard to believe.

When I think of high transition point amps I always think of Coda.  Take a look at the specs--and the build--of a few of them.

I think that is very optimistic too, I have a Belles SA30 class A power amp that has been measure more that 50watts and I can tell you that it gets hot, not warm, but hot, one can just touch it for a second or too before it gets very uncomfortable.
and it has big heat sinks and good ventilation holes on top plate and bottom plate.
as it sounds fantastic I can live with it as a heater at the same time 😉

So, guys, all I can tell you is this is what they told me. It has dual toroids but...I'm just a lowly humanities guy. If they're lying directly to a customer, that would be pretty wild. Of course, their native language is not English, but they're an international company. Whatever. Another mystery.

Yeah, there is no way that this amp is running 40w class A. To deliver 120w into 8 ohms, the amp probably has rail voltages of approximately +/- 46v. To deliver 40w RMS class A, you'd need a bias current of about 1.6A to allow the amp to deliver 3.2A peak while staying in class A (assuming a push-pull output stage which is the most efficient for class A).

Across the two rails, that's an idle dissipation of almost 300W for the two channels. To support that, you'd need heatsinks probably 20 times the size of the ones in that amp, and it would still get toasty - probably too hot to hold your hand on it.

A class A/B amp with heatsinks the size of the IN200 is probably biased just enough to prevent the output transistors from completely turning off near the zero crossing - maybe a bit higher. I'd be surprised if it would stay in class A beyond a few hundred milliwatts. 

If you want to get a flavor for what a class A amp sounds like, you should keep an eye out for a Pass Amp Camp Amp. These are sold in kit form in the DIY Audio store for about $330, but regularly show up on the used market in assembled form for $250 to $350. It only puts out about 8w, so you won't be able to play your current speakers very loud, but it should give you a good sense of what class A can provide.

It's also possible to bridge the amp and use two as monoblocks if you find you really like it and want a bit more power.

If you buy a used one, you should be able to sell it for what you bought it for after you've played with it for a while.