This is a heat sensor safety to shut the heater off because of trouble. Also some incorporate a fall over switch to turn off the heater if it is kicked over and could cause a fire . Either way if you are careful you can solder it. On both wires strip back a half inch of insulation and use a paper clip to hold the wires together so you can give the broken one a small twist around the remaining. It may brake off so do not get in a hurry we want to get the strains together as best as we can. Have on hand a wet paper towel for cooling the work when you are finished. On the broken wire move the strands down on the crimp. now apply lots of non acid paste to the strands and crimp. Warm this up with your soldering iron and let it drip off on a paper. Add more paste and start by melting your non acid solder to the soldering iron. You may need to wipe the tip to get a nice clean tip. Now with a nice blob of solder on the soldering iron tip move the drip into the strands of the wire away from the part and keep melting solder into the strands. Move your work down to the crimp applying solder as it flows into the strands on down to the crimp and dab your solder on it. You are actually using the solder to transfer the heat to the strands as your soldering iron can not touch and heat the strands to apply solder. It does not have to look good just affix the broken wire to the crimp and other wire. Because dirt and oil is the main cause of a bad joint I some times use a pen knife or a bit of sand paper to lightly scrape the parts. Sand paper for larger jobs but a little scrap on the wires and on the crimp here can be helpful if you are careful. I have done this many times and have tried to relate what I have done and written it as best as I can. Good luck with the soldering.