Best access to the T-stat housing is form the Bottom side, not the top. Now, while this was a full belt and water-pump job, I'm more just trying to show the location of the T-stat housing:



It's at 5 o'clock, the darker metal pointed down and right in the frame (and has the lower radiator hose on it in this photo). 3 nuts, evenly spaced.

As for the rest, I always take the opportunity to run some coolant system cleaner/flush for a few days before doing a swap, then do one quick flush with distilled water (10 minute drive, just get to temp to open the T-stat). Overkill? Maybe. For the "cost" of about $10 and 10 extra minutes of time it just seems like a no-brainer to me. I go Much more in-depth when I first buy a used vehicle (multiple cleaning flushes, multiple "rinse" flushes over weeks of time) because you have no clue what some PO did, or didn't do. My 4-runner had green coolant, and gooey globs that flushed out.