If not done properly, you'll risk twisting off the bleed tube. There is a 3/4" wrench purchase below the bleed skirt, at the top of the tube. Put an open-end wrench there and hold the tube still so it won't twist, then a 1/2" (?) on the screw and turn it. If it hasn't been apart for some time it -will- fight you. You might want to do this on a workbench when you remove the thermostat housing again, instead, so you can better see what you need to do and use more care, etc. If you damage the thermostat housing/bleed screw, shop for a replacement. Used and reconditioned housing are still available. I think we can still buy billet bleed screws.
When it's all back together, leave the screw off, then fill the radiator while gently pumping the upper hose - once full, dribble coolant into the bleed screw until it runs out of the filler neck on the radiator, then install a new #16 cap, then top off at the bleeder tube, then install the bleed screw. Add coolant to the expansion tank to the HOT line. After the engine heats up and goes thru at least one cycle of running the fan (low speed), let it sit overnite. When it cools back down completely, it should pull coolant back into the system and if all goes well, the level in the expansion tank should drop to COLD. Don't let the tank go empty or you risk getting air in the system and having to start over.
A code reader live-tests those circuits and their components (EEC, IRCM and fan motor) for you - takes only a couple minutes. The code reader will also help you decide if the ECT/harness is working properly/needs a closer look. You don't know you need an IRCM yet (don't guess), so you have time to keep looking. As I said, I see used ones on eBay at a decent price right now. You can also place an ad here in the parts wanted section. Don't look for one 'for the car'...get the part # off yours and look for it, instead.