I too own a '92 cherokee (but this post is of your '96)and water pumps either last a while or just suddenly start dripping. Thermostat change is 1-2 years on my jeep and that usually works . Question : are your back flushing the heater core ? When you flush the system , are you squeezing the lower radiator hose when filling radiator with coolant and water ? You must get the air pockets out . This WILL cause temperature rise RAPIDLY . For now. With engine cool , take radiator cap off and squeeze lower hose and watch for escaping air bubbles. You must squeeze in such a way that you are trying to push liquid in and through the engine to circulate the liquid back toward radiator for air to escape . This will take some time and your right hand will get quite a workout . But you must be sure to get all the air out . Keep the radiator topped off so that liquid volume will force its way into system and through to push liquid back toward radiator to push air out . As long as your system is air pocket free and circulation is good throughout ( radiator , heater core , hoses , etc.) and hot water valve for heater core is operational you can have a better idea of the engines condition. Are you losing coolant ? Any leaks ? Pressure loss at cap ? You want to be sure no pressure is lost and a good idea is to test radiator with pressure tester pump . If radiator cap is old , replace it , don't even bother testing it with pressure tester adapter if so . Only test a new or fairly new cap .
Lastly , I certainly hope the head gasket is not bad as if the coolant pressure is lost at cylinder head and is leaking past head and block or into cylinders and oil ports , you know what that means. Head gasket and cylinder head inspection for cracks . I don't want that for either of us. I have to add every so often and I still have to bleed air from my system from the last flush as my electric fan goes on when gauge is getting to 210 or over too . But prior to my last flush , was running cool . Please try getting air out and hope for the best . If this is recent , it may just be air . But must be done ASAP to avoid engine damage !
