I was replacing the thermostat on my car. As I was tightening one of the screws. It broke and the other half stayed in the hole of the part where you set the thermostat. I was wondering if the housing can come off so I don't have to drill out the broken screw while its attached to the motor!
Not clear on what the problem is. If the head is broken off and the other bolt is removed, of course you can lift the housing off. If part of the remaining bolt is sticking up you may be able to turn it with a vice-grip pliers. You can also slide a nut over it and weld it to the bolt, then use a socket and ratchet to unscrew it. I can describe how to do that even if the bolt is broken off flush. You'll need an acetylene torch, a wire feed welder, and at least one nut, maybe more.
If the remaining part of the bolt has already turned a little indicating it's not rusted tight you may be able to drill in the center with a left-hand drill bit and walk it out with that.