My approach is “b”
I always open it up to see what’s going on in there. Simple test in hot enough water to open them up. If it opens I keep using it. I don’t like running without at least a good used thermostat.
If it’s someone else’s motor I always check because someone may have already removed it and the motor will then run cold without it. If it costs me a seal or gasket to check it, so be it. Lot of times the seal is mangled in there anyways and needs replacing, or a lot of deposits and buildup that should be cleaned out.
