Don't need to drain it, just let it idle with the cap off and watch the fluid. Sometimes it helps if you give the upper hose a couple good squeezes to push some air out and suck some fluid up. My yukon takes 20 minutes on a 50* day to hit 210 idling. So I'd let it run at least that long to make sure the t-stat is opening. (this is assuming you don't have another problem.)
If you do drain it, throw a new t-stat in anyways since they're $5.
88 RCLB: LS swap in progress
00 CCLB
03 Yukon Denali: Wife's "soccer mom mobile"