Can you put a thermostat in the incubator itself?

[Blue Apple Herps]

You have to put the thermostat probe in the incubator in order to properly control the temps. If you mean put it directly in the egg tub, I do so I can know exactly what the temps are inside the egg box.

If you mean the thermostat itself, I wouldn't. Just run the probe/wires into the incubator. This way you can easily control it from the outside, plus it'll be operating at RT and not 90º.