I would just replace the thermostat, although the ECT is easier to get at when you have the housing off, if you have any doubts about it. When I replaced mine, I did not drain the coolant, just loosened the torx screws and let the coolant dribble out until it stopped (probably don't want to do this in your garage unless you have a wide pan underneath--also one post warned of getting the coolant into the alternator). Also didn't disconnect any hoses, just flexed the hose back with the housing attached, picked the old thermostat out and put the new one in. Then, top up the coolant with 50/50 mix suitable for aluminum engines (no phosphates)

There are some posts that warn of some difficulty getting the screws out, I had no problem and simply put a long extension on the torx bit for the back screw--they are tight though, so you need to put a fair amount of downward pressure on to keep the torx well engaged. Unless you run into problems should take you 30 minutes max.

I had to do mine out at an airport when the car suddenly overheated...
--
96 850T, Bilstein HD, IPD swaybars