1999 Jeep Cherokee(4.0-6 cyl)/Starts fine when COLD ,after running awhile starts hard(coughing and sputtering while pumping gas pedal ,then idle catches(reving high until returning to normal idle?Also while engine is warm,sitting in PARK a little while it will start to cough and sputter until stalling out ?

SOURCE: Stalls when engne warms up

Your ECT (Engine Coolant Temp) sensor is bad. What's happening is at cold start it richens up the fuel mixture and as it warms up the ECM thinks it's still cold and essentially the "choke" is still on. Also check your coolant level. If you don't have enough coolant in you engine/radiator, the ECT doesn't know what to do so it thinks it's cold.

SOURCE: 1999 jeep cherokee starts hard

have fuel pressure checked ...fuel pump maybe losing prime

SOURCE: 1996 Jeep Grand Cherokee stalls when brakes are applied

My 2000 Grand Cherokee had the same problem, without all the sputtering, it would just die approaching a stop. We could only keep it running by slightly pushing down on the gas petal when coming to a stop. I replaced the Throttle Position Sensor, but that didn't change anything. A new mechanic I found replaced the Idle Air Control Valve, and we've had no problems in a week.

SOURCE: 95 jeep grand cherokee, hard starting, backfires, when cold

get a couple bottles of gas line antifreeze .. if you don't already use it and add it to the gas.

Robert

P.S. in minus 40 i don't even get out of bed... minus 23 here last nite... isn't winter grand

SOURCE: after running the engine for awhile in stop and go

CHECK COOLANT LEVEL.CHECK THERMOSTAT.IF TOP RADIATOR HOSE DONT GET HOT IN 10 MINUTES AFTER FIRST STARTING CAR IN MORNING .AND JUST THE BOTTOM HOSE.THERMOSTAT STICKING CLOSE.IF THERMOSTAT FINE.PROBLEM COULD BE CLOGGED RADIATOR OR ENGINE BLOCK CLOGGED OR FAULTY WATER PUMP.