Heater blower is working but only blows cold air 2001 Grand Cherokee Jeep Limited 3.1d

I would make sure the core is the problem. You may have a heater control valve that cuts off flow to the core by vac. or a blend door that cuts off air flow thru the core.
You will need a shop manual to replace the core. The dash and console have to come out, along with discharging the ac.

Probably broken blend doors if everything else is working, but its just blowing cold air. Do a google search for "Jeep Blend Doors" or "Heater treater" for more info.

either bad recirc doors or a possible bad heater core. Open the hood and when the car is warmed up to mid point on the temp gauge look on the passenger's side firewall under the hood. You will see 2 black rubber hoses running through the firewall. Feel each hose and if one of the 2 are cold then you have a bad heater core. Otherwise most likely the recirc door.

You may have the blend doors problem which means the blend doors are in the closed position only allowing cold air. They need to be fixed. Google "heatertreater" to see full explanation and fix.

Could be the switch or the resistor.

It could be a poor seal but I've never seen it. What you could have is a fresh air door not closing properly. Fresh air door/recirculation same thing.

try flushing out the heater radiator core.remove the two pipes and put a hose on the conections and keep reverseing flow.dont forget to top up with pure antifreeze,

Change your Thermostat.

The blend door on the passenger side has broken. Jeep has made a replacement section for the heater box assembly so you don't have to buy the whole thing. You will need to remove the heater/A/C box to replace the part. I have done quite a few of these repairs to fix the problem

Check on Ebay for Jeep Grand Cherokee Harness Kit. The plug on your harness may be melted like mine was. I bought this kit, followed the instructions in his ad and it worked great. All I had to do was cut off my old plug and solder this one on. Even the wire colors matched so there was no guessing.