When my 92 Lesabre gets hot it will shut off..

Eloy, if the pumps are heating up, you must be running with very low fuel in your gas tank, fuel is a must to keep pump cool and lubricated or you are continually getting bad pumps. Clean tank thoroughly,replace the sock on end of pump, replace fuel filter check to make sure there are no pinched collapsed fuel lines.Try running gas tank no lower then quarter tank and buy a quality replacement pump and give it a try.
http://www.automotiveforums.com/t246788-overheating_fuel_pump_anyone_.html
Chevrolet Fuel Pump Failures Explained on YouFixCars com
http://alt.autos.gm.narkive.com/t828G3rB/why-are-gm-fuel-pumps-so-short-lived-class-action-lawsuit

Is the pump getting power from the fuel pump relay ?

check the fuel pressure from fuel pump it may be bad. its a possibility that the coils maybe getting hot and shutting down engine. but check the fuel pump relay in fuse box. to see if this is your problem. it could be getting hot and shutting down, just replace it.is the check engine light on ! if so you can go to auto-zone and they will scan it for free of charge. to find problem code. with OBD-II scanner. good-day !!

It can still be the fuel pump.the pump could be getting hot and not working. If u let it set for awhile and cool down it will start. You need to do a fuel pressure test it should read between 40 and 50 psi. Let it run for awhile and see if the pressure drops. If so I would replace the pump

This happened to mine and it was the fuel pump!

fuel pump falling apart and pieces going into your new fuel filter. You need to change both. I just did!

Did you change the fuel filter? A partially clogged fuel filter will burn up a brand new pump. Otherwise I would suspect you just got a brand new bad fuel pump. Has happened to me twice, so it is possible. Some parts I pay more for to get the OEM brand. Fuel pumps, water pumps, heater core, etc. Any hard to replace part, I buy from the dealer or from a parts store that sells the OEM brand.

Most likely a bad connector on relay or the fuel sock needs to be replaced. if the sock is plugged it would cause the fuel pump to work hard and cause it to heat the relay and make it hot and removing it will cause it not to run. check the connectors to the relay see if they are opened up in the female socket if they are use a dental pick to close them up with. otherwise replace fuel pump and sock at that age with the alcohol in fuel it's killed the pump and sock.

Check fuel flter at fuel pick-up intank (looks like a small wire sock). Remove fuel filter and fitting at fuel rail. Blow out fuel lines w/about 35lbs air press. Ck electrical @ relay - should be 4 connectors - one is key on hot/one is always hot/one is ground and last is hot to fuel pump. Good Luck

relay is under dash on driver side behind cruise control box. You tube has a demonstration on there for 92 accord.