What engine is in your Cutlass? I noticed you are in Florida, and that can be damn hard on a cooling system. If your car has had an engine swap, make sure it has a V8 radiator and NOT a V6 one!!! If it has a V8 radiator, make sure it is a 3 core at minimum. I would also at least put a restrictor plate in the thermostat housing. The fact that it came with no thermostat tells you something. It says that the previous owner probably had cooling issues as well. Remember that bolting an engine in a car is the easy part of a swap, not everyone knows how to engineer the car to function properly with the swapped engine. Plenty of half assed project cars get sold due to an inexperienced owner's lack of knowledge or money to get the car right. Also, do you have A/C and is the overheating problem limited to times when it is on? At any rate, if the thermostat does not fix it, it is probably time to get a better radiator. Look at a 82-92 V8 F body for a possible junkyard solution. You either want the 3 row copper brass or the Plastic/aluminum unit. The plastic/aluminum radiator is significantly lighter than copper/brass, bus be sure it s not old. If it is, it will eventually break due to the plastic drying out. One more thing: Be sure the air deflector is still in place under the radiator.
I do have one final question for you: When does it overheat? Is it only in stop and go traffic or is it while driving at a speed of 35mph or higher? Does it overheat quickly, or is it a slow process? How it is overheating can help tell you what is wrong. A car that overheats at speed typically has insufficient radiator volume while one that overheats in traffic may be suffering from insufficient flow. Remember that there are different loads placed on a cooling system depending on the engine's load, and airflow through the radiator. Even the car's hearing can affect cooling system performance if the system is inadequately sized to deal with the constant engine RPM's of freeway travel. This is why German cars have very good cooling systems.