No, a thermostat isn't suitable in most situations. Strictly speaking a thermostat is either on or off, and any time spent off, is time for the smell to drift.
You could use one to switch between two different speed regulators. Often this is done by switching between a trickle or having full speed if the temperature reaches the set point.
It's very rarely a good idea to not extract. Even a sealed room using co2 should have an extractor. Though it can't do anything other than create a low pressure area. Unless you actually let some air in. And thus through.
If your legal, and it won't give other undesirable visitors a clue, then I guess at times you could switch off. I'm scratching around to find a supporting argument really though. It's almost always something you should use.