All of the above is good advice. Just one old trick to add. On a new thermostat look for a small hole in the flat part that moves to open and close the thermostat. If you have one, good. If not drill one. That will let air move out and help prevent an air pocket forming. Your pump will move water. It will not move steam. That small hole will not hurt the thermostat and will help get air out of the system.

Steve H