Do the following, in order. (There are two parts to this.)
1) Check your fan clutch. (If the engine is hot, the fan should be hard to turn when the engine is off. If it freewheels easy, and you can spin it when hot, you need a new fan clutch. They are about 62.00 from NAPA.)
2) Is there coolant in your oil? Pull out the dipstick and look at the oil right after you shut down the engine. (If it looks like chocolate milk, it's BHG time.)
3) Does your car put out "white" smoke, or steam all the time, and can you smell coolant from the tailpipe? IF so, your BHG has arrived as well.
4) Do you blow out coolant when you boost? (Easy to check, just add a longer hose to the overflow port on the coolant tank, route it between your hood and fender, then drive and watch the hose sticking out when you boost. If it blows coolant when you boost, you have a BHG.)
5) Remove the oil cap when the engine is running. DO you have puff's of air blowing out of the cap hole? If so, you may have a BHG.
*** IF none of the above are a problem ***
1) Replace the thermostat to make sure it's working, and not siezed up closed.
2) Replace your pressure cap with a new one. (You can buy both at the same autoparts store while your buying the coolant etc.)
3) Fill with 50/50 mix of coolant and distilled water.
Then drive around and see if that fixed your problems. (You may want to clean up the front side of your radiator too, I've found most older Supra's have a trash dump of grass, leaves, pet hair and other crap packed between the condensor and the radiator, and you can't see it unless you pull the radiator and look. (This is also a good time to flush out your radiator completely with lots of fresh water and a hose. If you want to run "cooling system flush" go for it, and then pull the radiator and flush it out completely.)
Good luck.
I just had to replace my fan clutch reciently, and it made a huge difference in traffic. Also a few years ago, my thermostat failed closed, and it would peg the needle in a few moments of running the engine. It was sporadic, and drove me nuts till I just broke down and bought a new one and replaced it. (So nice when you finally figure out what's going on with your car.... Especially when the part you need is less than 10.00.)