Yup, I'll side with Tom on this, that's pretty much the way to tackle it, and it's really a pretty simple job once you get into it if you need to. While you have the T-stat housing off, might not hurt to have a new gasket on hand for the two halves and pop it apart for a stat inspection for wear or damage (they are known to break apart), maybe even a little housing polishing on a wheel.
Clean the bolts with a wire brush/wheel once they're off and apply some never seez before reinstalling. Better, cheaper, and far easier to fix it now as it is than to deal with the results of an overheat later.....