A relay has gone bad.
Jeep Cherokee's have 2 cooling system fans and one climate control fan. One cooling system fan is fan belt driven and the other one is electric and is turned on/off by the engine computer at about 215*. The A/C and heater fan is electric.
Check your local junk yards.
For the radiator electric fan... Depends which fan you're talking about ? The heater fan or the radiator fan ?
If its the fan speed your talking about its likely that the speed controller on the fan is broken and had its days
The wiring connector is melted. Check wjjeeps.com for pictures and a solution.
The coolant fan continues to run after the engine has cooled and then turned off. The fan continues to run and runs the battery down.
Check your cooling fan
Under the hood, on the passenger side firewall, close to the passenger side fender.
you may have leaves in the fan
When there are loose parts in the fan that runs the heater system, there will be many instances of noise and vibration. A technician should dismantle the system and fix it.
are we sure it is smoke not hot anti-freeze mist leaking from heater core ? if it truly is smoke you have a shorted fan switch.
The fan blades are most likely rubbing the sides of the heater casing. The fan could be loose, the motor bad, or the fan blades broken. There is also the chance that something (candy wrapper etc.) has been sucked into the system and is rubbing the blades.