No heat 2001 Grand Cherokee. Heater blows out cold air.

SOURCE: Heater blows cold air when idle

Sounds like you may have a partially plugged heater core. You could flush this out separately, from flushing radiator & engine block. Diconnect heater hoses going to your heater core and clamp off, so not to loose coolant from engine. Now hook up separate hose to one side of heater core pipe and flush out with typical garden hose. Repeat procedure on both heater core inlets. Reconnect original heater hoses and test difference. You may have to add an additional litre of antifreeze. If this don't work i suggest changing heater core. Good luck.........Ron.

SOURCE: 2001 jeep grand cherokee

You have the common 99/04 Jeep GC blend door problem.

A repair shop or dealer will charge around $1,000

There are do-it yourself blend door repairs on Ebay.

SOURCE: 2001 jeep grand cherokee heater problem

BLEND DOOR FOR RIGHT SIDE BROKE INTO THE A/C SIDE. TO REPAIR PROBLEM WILL NEED TO REMOVE DASH AND HEATER/EVAP CORE BOX.

SOURCE: Heater blows cold air

If the "Heater In Hose" gets hot, and the "Heater Out Hose" does not get hot, than either the Control Valve is sticking closed, or your heater core is plugged up with ****!

Have you used "Barrs Leak" or a simular product for a radiator leak? That will sometimes clog the heater core.

I have a 1993 Grand Cherokee, which "Normally" throws very hot air out of the heater, but lately sometimes it only throws warm air, till I make my first stop, than it gets hot.....all because the heat control valve is hanging up.

Low water in the radiator will also cause a heater to not work.....if the water level is too low to circulate to the heater.

XRM

SOURCE: Why doesn't the heater blow hot air?

If your "Check Engine" or "Service Engine Soon" light is on, you need to have that checked out first.
If not, the next thing you should check is your engine coolant level. (Antifreeze) If the coolant level is low, the engine coolant does not circulate through the heater core and the the heater doesn't work. The coolant level could be low for a number of reasons including a leaky hose, water pump, or head gasket. In any case, if it is found to be low, you need to find out why.
If the coolant level is OK then the thermostat function needs to be checked to make sure that the engine is reaching operating temperature.
If all of the above checks out OK, then the heater control valve and/or the blend air door in the HVAC housing needs to be checked for proper operation. (NOTE: some cars are not equipped with a heater control valve)