7mgte overheating problem

I recently bought a 87 supra with the 7mgte. ive been driving the car for a little over a month with no problems. About a week ago it started running warm when its sitting. As long as the car is moving the temp stays normal but when you stop it starts climbing. Ive read a lot about the dreaded blown head gasket problem and I just wanted some advice before I try to replace it. I'm not sure if the head gasket is the problem, ive checked the oil and it doesn't look milky. I have also replaced the radiator and when I drained the old coolant it was pretty clean. was just wondering if it may be something other than the headgasket. Any advice would be greatly appreciated! thanks!

1. Are the fans working ? Is there debris in front of the radiator, blocking airflow?
2. Sticking thermostat is another issue. Big difference in the temperature of the upper & lower radiator when the temp rises, is a good indication of a failing thermostat.
3. In park/stationary & the temp starts climbing, but raising the RPM brings the temp down somewhat consistently. That's an indication of a failing water pump.
4. Using a coolant pressure tester to check for combustion into the coolant. Connect the tester while cold & off. Start the vehicle. If the pressure climbs quickly, within the 1st 5mns especially, more than likely you have a head gasket issue.

Hope this gives you some direction. Post an update with you're findings.