If your temperature gauge seems to move in its own mysterious manner, or the warning light blinks on and off at will, then you may be getting and indication of the internal workings of your motor. Somewhere down the line, unless you've got a faulty sending unit (see the Gauges section), there's a problem with the car's ability to cool itself off. And that's not a good thing at all.
First thing to check: make sure you've got enough coolant in the radiator. It's a common sense thing but it can happen. Also, check for leaks around all the hoses to the block, to the radiator, to the overflow bottle, and to the water pump. If you're getting a little puddle of green on the driveway or garage floor around the center of the engine, toward the front, that usually indicates a bad water pump. All water pumps are designed with a built-in weep hole on the bottom. When the pump itself goes bad (usually because of a bad bearing), it's designed to leak antifreeze out the weep hole to let you know this. You can put your finger on the bottom of the water pump to feel this and confirm the problem.
If it's not any of the above, the next thing to do is get the car warm. What you're looking to do is see how the thermostat operates and the general flow of the coolant. Take the cap off the radiator when the car is cold, make sure the fluid level is full, then start the car. Leave the cap off for now. It will take about 10-20 minutes, depending upon outside temperature, for the car to get warm and the thermostat to open. If you have a temp gauge, you can keep an eye on it to see where you are. You're looking for the fluid to drop all of a sudden, and the fluid to jet out of the rows inside the radiator. You may need a flashlight to check this. When this happens, the thermostat just opened and the cooling process has begun. This is normal. If the car is warm but no coolant is moving, or is moving but very slowly, there are several more things to check. You may have a bad thermostat, bad fan clutch, clogged radiator, or (worst of all) bad or clogged heater core, even a blown head gasket. At this point, if you're not mechanically inclined, you might want to have a repair shop look at your car.
One thing to point out is that your gauge or light depends on a sending unit. It is entirely possible that the sending unit is simply bad from years of usage, and simply needs replaced. For not much money it's very cheap insurance, and it may possibly solve the problem, although if it doesn't then you can rule it out.
The dreaded thermostat is a likely cause of overheating. Especially on the 5.0 V8 engine, it's a bear to get out. The 2.3L 4-cylinder and the 3.8L V6 cars are a little easier to get to. You can test your old thermostat by boiling it in water on the stove, and observing the approximate termperature that it opens. It should open a few moments before the water begins to bubble/boil. If it doesn't open at all, there's the problem. Again, very cheap to replace. Don't forget to buy a water neck gasket and some RTV silicone to go with it. And we would highly recommend getting a heavy duty thermostat. It's only a dollar or two more than a standard thermostat but the construction is much, much better. Stock thermostat rating on the 3.8L V6, 5.0L V8 and 2.3L I-4 is 195 or 197 degrees F.
Fan clutches are known to go, so that's also a good place to look. This controls the action of the plastic fan blade when the car is moving, and usually kicks on at low speeds or at idle. When the car is cold, the fan clutch should spin around clockwise approximately 1-1/2 times before you feel it resist you. That's normal. If it keeps on spinning, you've got a bad clutch. A fairly inexpensive part.
If you don't make a habit of getting your coolant system flushed every few years, then your radiator's internal rows could be all gummed up. A clogged radiator will play heck with you. When observing the thermostat opening in the car, pay attention to the speed at which the water comes out of the rows. It should gush out fairly quick. If you're getting a trickle or nothing at all, that's probably the problem. New radiators are not cheap (usually start at $150 US) but the old one can be re-cored. Also, the warranties on most new radiators are only 1 year, so be aware of that. People living in the southern parts of the U.S. (especially the southwest) should purchase 3-row or aluminum radiators to better combat the hotter climate. You can generally use any Fox-chassis radiator in your car, as long as it's made for the same type of transmission that you have. If you'd like to get a Mustang hi-po aluminum radiator, go right ahead. The price of three-row and aluminum radiators have come down significantly over the past few years so it may be worth the extra money to get yourself one of those.
If you're getting a slimy film on your windshield from the defroster vents, or you're getting a lovely wet puddle in the passenger side footwell under the dash, you've got a bad heater core. Besides changing an oil pan, this has got to be the absolute worst thing to change on the entire car. Click here to see full instructions on doing this.
There is the possibility that you've got blown head gaskets. For more information on this problem, click here. Worse case scenario, you could have a cracked head or a cracked block.
Hopefully these hints will help you narrow down the cause of your heating and/or cooling problems. While it's not an exact science to do so, a little trial and error will gain you a ton of experience with handling the problem in your car.