Check the hose on the back of the head, it's a 90 degree black rubber hose, if it didn't burst, then you better go ahead and replace it now, along with the fitting it's connected too if it's erroded (most likely). That one is bad about going out if it's the original one. You will overheat very fast if that one goes.
I suggest parking your car for now and start on basic maintenance because from what you've said, it's got some issues and needs some TLC. Remember, this car is old, parts need to replaced: Start with Rubber hoses, check them for cracks, dryness, etc. Squeeze them, inspect them carefully, it they look bad at all, replace them with genuine Toyota parts. That's about the only place as of right now to get replacement parts for the Supra when it comes to hoses.
You can replace the Vacuum hoses (all of them, you should do this now as well) with some thick silicone hose, or new rubber hose will do.
Belts, replace them.
Your clutch fan, search on this site for a thread detailing how to rebuild it, yours probably needs it.
Check the radiator to make sure it's not blocked or clogged anywheres, have a radiator shop do this. If it's corroded, replace it with a factory type replacement, or an aftermarket Aluminum radiator (I would personally do this). DO NOT use regular coolant from Wal-Mart in the motor, buy some coolant flush and run it through the motor. Then use either Genuine Red Toyota Coolant, or a HOAT type coolant, google that one for clarification.
Replace the t-stat with a Toyota 190 degree t-stat, or a Stant Superstat (you can get by with a 180 degree one, but it's not going to make the car run cooler, just take longer to heat up to operating temps, which can be a bad thing if you only make short trips in the car).
Re-torque the head bolts to 72 ft/lbs, first crack them loose per TSRM specs, then Re-torque them in the correct order.
Do these things first, this should keep you busy for a while and your wallet empty. DO NOT start modding the car, it will bite you in the ass. Don't drive it hard, in fact, hardly drive it until you've done ALL of the above. Trust me, you will thank me later.
