I did it myself a few years ago and I replaced my 87C tstat w/ an 80C version. When I removed the old one, it was 'stuck' open so that explained why my car took a long time to warm up. Now it warms up w/ 5 mins or so.
That short rubber elbow . . . it still can get my BP up just thinking about it!

I didn't lube the rubber and you can get a picture of how hard it was to get on w/o 'lube'.
After I did get it on, after many scraped knuckles! Later when I was at my tech's shop (Exclusive Motors), he was replacing a water pump. When he came to replace the elbow, he, of course, lubed it . . . and . . . used a small right angle 'tool' that he could reach around the back side, grab the backside, and slide the %#*^@! on within two seconds and no scraped knuckles! Live and learn I always say!