Heater Core in Jeep Grand Cherokee 1999

Unfortunatly, those are the classic symtoms of a bad
heater core. But just to be sure, check the heater hoses at the firewall and make sure that a loose clamp is not allowing coolant to spray into the car.
I don,t know what the part costs, you can find that out by calling autozone/napa or any parts store.
But there probably will be a slight markup by who ever is to do the job. As for the labor, the book allows
5.9 hours for the job. This will give you a place to
start when you check around for the best price.
If you have a mechanic that you use often(and trust)
ask him/her what it will cost. It's not strictly dealer.
Hope this helps.