Thermostat and/or heater core may be defective
One of the reasons a 2000 Jeep Cherokee heater would randomly blow cold air and then hot air and then cold might be that there is a problem with the hot/cold duct. The air or a vent might be inadvertently blowing periodically.
Bad thermostat
It could be your heater coil needs replaced. Expensive to have fixed though. Or it could be something as simple as low anti-freeze. Suggest you take it to a mechanic/garage.
probably air in the system have you replaced the rad or hoses?
Most common problem is that the blend door is stuck or broken.
The thermostat could be stuck closed. the heater core could also be plugged or the door closes when you use ac and opens when you use the heater may not operate.
The HeaterTreater is an after market kit that solves heater and AC for the Jeep Grand Cherokee and Laredo. It is much cheaper than the dealership fix and is easy to install. For diagnosis and info, check out www.heatertreater.net or search eBay for "heatertreater".
seperated tires or obstacles on road.
It mite not be a fuse have you checked the vacume hoses that come from intake manifold this can cause the fan not to blow.
You may have a faulty expansion valve. It may prevent compressor from running long enough to cool your car.
run as fast as you can cause it is going to blow up in 5 minutes
My 89 jeep Cherokee surges at idle and sometimes stalls but runs fine once you are going what could cause this?