I believe Gene was referring to the thermal fuse on the heater.

Many units also have a thermal fuse on the blower. It kills power to the entire unit. Usually a dirty or malfunctioning vent system causes this one to blow.

The below is for the heater fuse.
If it is blown you have to find out what caused it to go.
Note: that sometimes they do just blow on their own but changing it without checking other things is a gamble.

Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it.

If the above is OK then you will also have to replace the hi-limit as it should have regulated the temperature so the fuse did not blow.

You still have to find out why it blew.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).

[COLOR="Blue"]Could a weak/failing high temp sensor be the cause for this to fail?[/COLOR]
The heater thermal fuse should not have blown if the hi-limit is OK.

[COLOR="Blue"]And should I simply dig back into it and replace it anyways?[/COLOR]
I would.
But you also have to find out what caused the unit to overheat in the first place.
Since it is gas I would put the operating thermostat at the top of the list.