The "thin filament" is the heating wire. The braid I spoke of is on some heaters and is for mechanical strength. The braid wraps around the outer insulation of the heater. Your heater may not have a braid.
If you have a multimeter, do the following:
1. With the heater unplugged, measure Ohms from one black wire to the filament nearest it. Give it 10 seconds or so for the effect of the inductance to peter out. It should read 0 or 0.1 Ohm.
2. Now measure Ohms from the same black wire as above to the other filament near the other black wire. You should see a much higher resistance. If it is OPEN, then you may have cut through the heater module, which is where the filament contacts the first black wire. There is a way to fix this, but I'd have to see the heater in person to make that call.
The unit you have does not have polarity, which is why the wires are both the same color. If the results from 1 and 2 above are like I said, then you can hook up the power cord HOT (blk) wire to one of the heater wires, and the NEUTRAL (wht) wire from the power cord to the other heater wire. If the module contact point has been broken, then the unit will not heat or only the last module length will heat. Module lengths are often in 3ft intervals.
-----
Mark G
Montane snakes are the coolest...