Either you have been buying bad TDMs, or you have a short to ground somewhere in the system that is overloading it and causing the instant failure. Not much else in the system really.
Without the TDM installed, you shouldn't be having any overheating issues as the fan should be engaged 100% of the time. Only thing that would change that is a bad cadillac valve.
The fan will still move air at idle with it disengaged, but wouldn't be anywhere near as much as with it fully engaged.
The fan system defaults to engaged if it doesn't have any voltage to it. The only ways to fail to disengaged are either the temp switch on the motor or the TDM failing and providing 24V to the cadillac valve, or for the cadillac valve itself to fail and jam open. Most common of these is the TDM, after that is likely the engine temp switch. Most cadillac valve failures I've heard of were preventing the fan from disengaging, not the other way around.
If the gauge is still showing 240V with the TDM removed and confirmed that the fan is fully engaged (in the manual it pretty much just says rev the engine and see if you feel a lot of air coming out from under the truck by the driver's door) then you need to do a couple things
1) use a laser thermometer to verify the engine temp. The metal right next to the thermoswitch for the cooling fan, or the upper radiator hose right next to the block are common places. This is to make sure you don't just have a bad gauge or sender
2)Check the radiator temp. Once everything is warmed up the thermostat should open. If it doesn't open, then the engine coolant just isn't able to get rid of the heat. Again, a laser thermometer should work.