Need help replacing cable to rear window heat

Excuse me in advance for maybe not being able to explain this in the most perfect english but here we go:

We've got a 407 SW and I need to replace the cable that goes to the heating wires in the rear window. The cables has shorted out and caused somewhat of a cable burn as you can see from the picture (the red cable). My question is: what is the black thing on the middle of the cable? Right next to the burnt piece. Is it some kind of connector or does it do anything to the current going through it, a resistor or something like that.

Also, the plan is to just cut the wire right before the burned part and replace it all the way and attache it at new to the point at the window where it says rouge. Do you think I can glue it to the window with a glue that is conductive or does it have to be soldered? It's a bit hard to do without detaching the window so I thought I'd give it a go.

The picture is take with the lid taken of and the break light detached.