I third the thermostat suggestion. It’s a real easy part to replace and on most cars is at the top of the engine. If I remember correctly, you’ve got plenty of space to maneuver in the engine compartment of that 1984 300 zx.
If you are going to replace the thermostat yourself, make sure you completely scrape off the old gasket (trying to make sure none of it falls into the cooling system).
If your coolant is full I would switch out the thermostat first. If you are actually loosing coolant, you may have another problem.
Once your car has cooled off, open the radiator. If the coolant level is low, fill it back up to the top.
If you are loosing coolant but there is never a puddle under the car, there are two possible problems.
1. There is a small leak somewhere but the coolant is burning off of the engine before it hits the ground. i.e. maybe a small crack in the upper part of the radiator.
2. One of your piston rings is slipping and your engine is sucking coolant into the combustion chambers of the engine. Typically this leaves a light gray residue on one or several of your spark plugs.
If you continue to ride around while your engine overheats, you run the risk of blowing your head gasket. While it’s easier to replace it in the 300 zx then most cars, it’s still a royal pain in the ass. Make sure that when your car overheats, you run the heat in the car (even if it’s hot outside). You can also spray the radiator with a hose to try to cool it down quickly.