Beverly,
An overheating engine can have many different causes. So, since you said its not the thermostat, we'll rule that out. Here are a couple things to keep in mind when diagnosing exactly what/where the problem is.
If your coolant level continuously goes down and your temperature gauge needle rises into the "red" zone, you definitely have a leak somewhere. It could be something as simple as a loose hose; or something more substantial like a radiator or water pump problem. If you have never replaced the water pump on that car, you may be due. The cooling system with that engine is extremely good; but itís the pump that makes it good. When the pump goes, youíll loose pressure in the cooling system, which will not allow for adequate cooling.
Another thing to be aware of is the temperature inside the car. When the engine warms up (test this before it starts to overheat), turn the heat on max. inside the car. If the engine temperature keeps going up, but the air blowing in the car is still relatively cool, you could have a blocked heater core. There is a another little ìradiatorî behind the firewall of the car where hot coolant passes through. A fan blows on this radiator and that hot air is what you feel when you turn the heat on in your car. If this is plugged up, you wonít feel much (if any) heat inside the car's cabin.
Your brother may be on to something when he said itís the "heads". Whether he knows what heads and why, thatís another thing ;-) The '92 Diamantes had a nasty little problem wherein the piston rings and seals would wear away prematurely under normal use. When this happens, you start to burn oil, the friction in the engine builds up, and the cooling system may not be able to reduce the temperature. Be sure to check your oil level to make sure your car sustains its oil level under normal driving conditions. If you notice bluish smoke or detect a burning, oily smell when you walk around to the back of your car while it's running, you're definitely burning oil.

If you feel none of the above could apply to your problem, I'll go into the simplest causes of overheating (other than a coolant leak). It is possible you do not have the correct water/anti-freeze mixture in you car. Normally, when a coolant is added to your car, it consists of 1-part water to 1-part anti-freeze. If there is too much water in you system, your car could very well overheat (or completely freeze up in the cold). Another simple cause of overheating could be an over-tightened hose clamp, which could restrict coolant flow, thus overheating. Along those same lines, there may be some sort of physical blockage in your system. As coolant in your system ages, it starts to pick up a lot of dirt and debris. That starts to form into big clumps, which could eventually block a main hose. Think of it as too much 'cholesterol' in the car.
If you haven't gotten a coolant flush in a while, this would be a good time. It can be done yourself, but a mechanic could detect leaks if, indeed, there is one.
I hope I had some helpful suggestions for you, and good luck!