The problem is with the wiring that jeep uses, to small of a gauge wire for the job. The blower motor bushings wear out in time, causing the motor to pull more current than the switch can handle. (Melted switches and wires) Adding a relay between the switch and the blower motor resistor WILL fix the problem. Mine started with the third speed setting and moved up to the fourth setting. I added two relays, one for each of the highest settings. This is how you can fix it once and for all.
Parts used for the mod so far are: 40 amp relay, relay socket, some 12 gauge wire, solder, heat shrink, and a few 10-12 gauge butt connectors.
The wire for the 3rd fan speed is light blue on my '01 TJ. I cut this wire just past the switch. I extended the switch side of the light blue wire with a short piece of 12 gauge wire which I connected to terminal 85 of the relay, this provides the signal to energize the relay. The other side of this wire goes to the resistor block, I extended it with a short piece of 12 gauge wire that I connected to terminal 30 of the relay, when the relay energizes a ground will be applied to the resistor block through the light blue wire. 12 volts is needed for the relay to energize, I got this from a 12 gauge wire that I ran straight to the battery and connected to terminal 86 of the relay. I've connected a long piece of 12 gauge wire to terminal 87 of the relay, this will get attached to a good ground somewhere under the dash. That should complete the installation. I've burned out position 3 on the switch twice and I hope this will prevent that ever happening again. I may even go ahead and throw a relay on position 4 as well. Positions 1 & 2 don't see as much current as either 3 or 4 and should be fine without the mod.