I thought they tended to fail closed because some of them have a tiny hole so some pressure can escape. I had one that failed partially closed or partially open ,which ever you prefer.
I guess it depends on the type of t/stat .
As to the OP problem. 1st thing see if you are getting pressure in the system by feeling the hoses when hot. The t/stat takes about 5-6 minutes to open ,you can ascertain that by feeling the hoses on the outlet.When they go warm you know it has opened.
If you have good pressure ,no leaks ,t/stat opening etc, then its time to look at the fan clutch. It should have resistance so that when you spin it by hand it will stop when you hand is removed.
If thats ok I would look at getting the radiator cleaned by removing the top and bottom tank and having the cores rodded so you can see one end to the other.