You need to check for "trouble" codes with a scanner that can read all of them. Readiness won't set if there are problems. Yes, for sure thermostat has a lot to do with emissions and could affect the readiness for any test that needs to see the engine temp.
If you have a good scan tool you can run the evap system test manually. (Maybe even do a oxygen sensor test manually too but I'm not sure about that one.)

__________________
1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)