As I understand it, tanks put out an amazing amount of heat while in operation. In order to be a thermal chameleon, (and say, look like a snowbank when in reality the thing is extremely hot) that heat has to go somewhere other than the skin of the vehicle or the immediate environment. So, I wonder where they put it...

For the United States, it's probably not worth the money.
As I understand it, tanks put out an amazing amount of heat while in operation. In order to be a thermal chameleon, (and say, look like a snowbank when in reality the thing is extremely hot) that heat has to go somewhere other than the skin of the vehicle or the immediate environment. So, I wonder where they put it...
The tank doesn't try to look like something cool, but tries to look like something hot...
The idea is to confuse the enemy momentarily (which can make all the difference in modern combat), not make the tank invisible.
"Adaptiv -- an armor encasing that looks and feels as one imagines a dragon's scales to -- turns tanks into chameleons, allowing them to disappear into the environment behind them or to even look like a snow drift, trash can, crowd, or a soccer mom’s station wagon."
(emphasis mine) That quote should speak to this point.
Tanks are big, and hot. Cars are small, and, as I understand it, much cooler. Perhaps I am wrong, but I'd expect the total heat off that tank to exceed most of the civilian objects it is likely to try to mimic. So, where does that heat go?
And that's just considering the body of the vehicle. Hot exhaust from engines shows up on IR too...
I'm not worried about combat effectiveness. I'm just curious on the technical question of where the heat goes. You can use a sink for a little while, but when the tank's run by the equivalent of a jet engine, that's going to only be a little while...

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.