Have an 86 cadillac seville which was ran dry on coolant and overheated. wife drove it the rest of the way home and told me that the cars overheating warning came on 3 or 4 times where she had to pullover and let it cool down. what kind of damage is likely been done?

have you changed the thermostat, check the rad cooling fan operation, checked coolant circulation, check for coolant leak, checked for head gasket problem, checked for a restriction in the cooling system. you don`t say what if anything you have done to eliminate a cause.

i would have to say ck. the easast things first,when was the last cooling system flush making sure all cooling system parts are clean and new coolant added(old coolant looses its abilaty to work properly when old)then have the thermostat ck to make sure it opens and closes at the proper temp.

Someone would need to test the system and find out at what point the engine is overheating.
Is the thermostat not opening - is the coolant not flowing - or are the fans not coming on when the coolant reaches 220 degrees ?

YOUR LOWER HOSE LEAK COULD BEEN WATER PUMP WEEP HOLE LEAKING.OVER HEATING PROBLEM COULD BE WATER PUMP GOING BAD.MAKE SURE YOU HAVE CORRECT AMOUNT OF COOLANT IN COOLANT SYSTEM.

The most common overheating problem with the Northstar engine is a blocked purge line. It's job is to purge air out of the cooling system.
There is a small diameter hose coming from near the top of the coolant tank,this is the purge line.
With the engine idling,pull the purge line from the tank,if there is no coolant flow from this small hose,it is blocked and this will cause overheating.If the hose is clear, check for blockage at the nipple on the tank.Or trace the hose back until you find the blockage.The hose goes in to the engine to a crossover and comes out the other side to near the thermostat housing,the blockage may be there.

are your fans or fan working if not it will get hot. I assume you have electric fans or fan if so make sure when it starts to overheat the fan or fans come on if not check the fuse for the fans or relay, breaker, wiring itself.

Sounds more like an ignition control or coolant flow problem. Or, a/c fan not coming on with a/c.
Getting the water pump question out of the way, the pump either works or not. If it leaks it will cause an overheat due to coolant loss on flat ground or grades...doesn't matter. If the pump bearing or seal is bad it will still pump, it will just be loose and noisy. Coolant flow through the radiator is also essential...I don't think you have a problem there because generally this happens with less maintained higher mile cars.
A bad map sensor can cause your problem because it changes both ignition timing and fuel mixture, either of which can cause very high temps in combustion chambers especially when under a load. Mass air flow sensor can also do this but usually will cause idle problems. If fan is not on with a/c if the remainder of your cooling system may be enough to maintain decent temp control but cannot do this under a load. A/C turned off removes some load and therefore allow you to get up hills. Operating marginally, you can be pushing some coolant out of the system at times without even knowing it.
Now, about your engine: These engines are in my opinion a very poor design to begin with. Even with the best maintenance and low miles, they don't handle temperatures well. at this point, I'd be concerned that after repeated overheats and near overheats, your head gaskets may have started to fail, even though they were not the cause of the problem.Keep that in mind.
Have the items I mentioned tested. If you finally have the problem solved I suggest you change the thermostat as well...Overheating makes them unreliable.

why did it overheat?? don't use water in system will errode the aluminum heads.

Coolant temperture sensor is the first thing to inspect.
With the engine off and cold.
Pull the connector and clean it.
Check is this the OE sensor. It will have on of the following number on it.
10045847; 12146312; 15321686; 15326386; 25036092; 25036708; 25036979; 25037182
Write any number down, You will help you to get the EXACT match in the auto part store.
The sensor is around $15.
If the contact cleaning does not help then just replace the coolant temperture sensor.
Use the water pump thread sealer to ensure proper seal.
After install the sensor,inspect for ANY coolant leak before put the vehicle back to service,
Please post more information or question on the comment window.
I will follow this post.

You did not give many details, could be a number of things, start with thermostat change, if not let me know and we can go on to other things. Good luck dont forget to rate.