Starting Problem My 98 Ford Escort starts fine when the engine is cold, them it runs 20mins and quits and will not restart until engine cools down.

when it stops check to see if there is spark. easy way is to spray starting fluid into intake, engine side of air cleaner if possible. Easy does it,1-2 seconds. try to start, and if of nothing, coil or coil packs is the place to start. They commonly work when cold and quit when the get hot until they quit altogether.

try the tps sensor check for vacuum leaks

the cooling fan that comes on when the AC is turned on isnt working

If it starts fine when cold or will restart after it cools down and run until the engine warms up, have your TPS (Throttle Position Sensor) replaced. I have seen quite a few lately that will "warm" up and cause the car/truck to gradually run rougher as the engine compartment heats up and once it sits and cools off will restart and run again. You can go to auto zone, advance auto, etc and have them run a free diagnostic test on your car and tell you for sure if any TPS trouble codes are stored

check engine coolant temperature when it gets warmer, or at operating temperature, and verify that the temperature gauge is showing warmed up to operating temperature. If the coolant temperature sensor tells the computer the engine is cold it will over fuel and miss and the engine will die. When cooled down it will run fine until it warms up. Also could be coil if it starts missing after warmed up.

Dear dsmalley427,
I think it sounds like a fuel injection problem. You get fuel for a while until the injector backs up and then all of a sudden NO FUEL. The engine quits and the pressure drops and flow returns enough for you to restart. If I were you I would get to a good mechanic and check the fuel injectors.
OR--try adding a fuel additive that would clean the injectors.--Signed jwr

check fuel pressure regulator.+ vacuum lines going to it look see if gas in vacuum line.if so regulator rupture.

you say the engine shuts down when it gets hot if it runs rough before doing so it could be the coolant temperature sensor allowing the engine to  overfuel  if the engine cuts out in a couple of seconds but sounds smooth it could be the fuel pump , if it cuts out instantly its electrical.

1998 ford escort sport engine started making a tapping noise and engine light started flashing. Had oil and water at normal level.
Car has 110,000 miles. Been serviced regularly!

sounds like a dodgy mis reading of a sensor caused by electrical resistance which is turning choke on and flooding engine.know the fault but without car in front of me its difficult to diagnose,could be auto choke sensor which is on right hand side of cylinder head ,but not sure.best is probally dealer have you tried spark plug gaps ??25th although this would cause problems with cold starting not hot starting but its worth a look