The bad news is you will wish you did the T-stat when you did the timing chain, as you were right there!
Also, I agree with your thinking, but no guarantee that thinking the way I think is a good thing.
Good luck, keep chipping away at it!
1989 560SEL (172k)
1989 325IC (122K)
2004 Suzuki Volusia LE (3500 miles)
2005 Yamaha Road Star (20 K miles)