This was a very common problem with the original modules in this vehicle. Luckily, there is an updated module that now also comes with a new wiring harness that addresses the heat range and tolerance. You can typically find the resistor module online for 80 or 90 dollars (make sure it's the updated version or you may just run into the same problem again down the road, and as well, pick up a new updated wiring harness. From there if you're handy it's a snap. The resistor is held on by two screw. Undo the screws to free the old one, and then undo the wiring harness on the one side (red/black wires)...and snip off the other side's wires. Take your new harness and solder the new wires on, then attach the actual module's wiring harness, screw the two screws back in and you should be back to normal.
Heater motor switch and or the connection at the switch is melted. Also check connections at the blower motor and blower motor resistor for melt down damage.
the resistor has melted the variable settings. Replace resistor under passenger dash.
by the blower motor there is a resistor connection, you will find it melted the blower motor is bad. it draws to much power causing the connection to get hot and melt and burn. you will have to change the connector and the blower motor. the blower is still working but its drawing to much power, the motor windings are shorted out inside. disconnect the connector from the resistor and you will see it.
Check the resistor pack on or near the fan , it may have melted and needs to be replaced.
Normally the wires and plug in can be purchased at the GM dealership. Will have to cut the wires back if they are melted and solder the wires together. Can also use a heat shrink butt connector to connect wires. Recommend the heater resistor be replaced and the heater blower motor be checked for wear or noisy bearings.
Assuming there is no blower speeds at all, check the blower speed switch and the electrical plug into the back of it. You may find the plug melted. The switch and plug (pig tail) are available from most parts stores.
Examine the back of the switch for loose or melted connections. Then examine the resistor for burned spots. In most cases a burned resistor is the result of a failing blower motor. So if a new resistor burns out in a short time, replace the motor also.
The blower motor resistor is the common failure. It comes with the wires attached that plug directly to the blower motor itself. If there is another wiriing harness that is damaged then you will have to buy it too. The resistor failure has been linked as the only cause of the melted wires other than the blower motor itself. The motor can be tested with 12v power to it and it should run on high speed when tested.
If you have no blower speeds at all, first check the fuse. If the fuse is okay I would suspect the blower speed switch and its electrical plug has melted. If the switch checks okay I would suspect the blower motor is bad. If you have high speed only, I would replace the blower motor speed resistor. If you have all lower blower speeds but no high speed, replace the high speed relay.
Check the resistor pack on or near the fan , it may have melted and needs to be replaced.
The wiring connector is melted. Check wjjeeps.com for pictures and a solution.
The heater blower switch and the electrical plug attached to it may be at fault. Remove the heater control unit from the dash and inspect the plastic electrical plug attached to the blower switch, you may see it has melted. The switch and plug is available from your local auto parts store.