So, you have 3VZ, I assume...
First of all make sure your fan(s) kick on. I hope, 3VZ is similar to 1MZ even though the fans are hydraulic. So, if you turn on A/C - does your fans turn on?
If yes, then fans and relay are ok.
Next step is to find ECT Switch. Go to camrystuff.com and download the manual for Lexus ES300 93 - it has the same engine as yours. Locate the ECT Switch and disconnect it. Fans should turn on instantly.
If it is so - you might have a bad ECT Switch. That manual has a procedure to test it continuity in different temperature conditions, perform them before buying a new one.
Other possibility is air trapped in the system. Did you bleed the cooling system after all of those repairs? With heat set on Max? What is the temperature of air coming from the heater, btw - warm or really hot?
As to the head gasket.... Several ways to make sure it is or not so. If HG is busted coolant may turn into crap looking substance. You may see milky stuff in your oil. Your spark plugs are wet. Your compression is low. Finally, you can do pressure test to the cooling system to see if it holds the pressure.
Yeah, and

to TN!