It actually took two tries with the screw extractor. It was in and working where the bolt broke during the first try. The picture is from the second try so you only see half of the bolt that had to be removed.

It was just seized in there. The back side of opening for this bolt is open so I could have used a bolt twice as long with no problem.

 

Glad you had luck with it.

For future reference, the BEST thing I've ever used to extract a screw is a left-hand twist drill bit. Drill a hole in the center of the bolt with the bit, and usually, the bit will grab and spin the bolt out (since the drill bit spins CCW). If it doesn't remove the bolt, at least you now have a hole in it to use a screw helical screw extractor.

 

I think the easiest thing would have been to remove the thermostat housing again so you have lots of exposed bolt to work with. The bolt holes on the Tstat housing should be unthreaded, so if you undo the other bolts should pull right off, exposing about .5" of the broken bolt.