I have a halogen heater and one of the bulbs in it started flickering so I opened it up disconnected that bulb and found the casing around one of the wires connecting to it was burned off. So I have this exposed wire which is not connected to anything and was thinking about just covering it with duct tape and using the heater again. Now im not stupid and everything about this to me sounds like a bad idea but would like to get a second opinion on exactly how dangerous it would be, it would only be temporary until I got a new heater.
the real question to be asking would be why did the insulation burn off in the first place. but anyway just use electrical tape to cover them. as long as the heater has a ground prong on the plug (3 prongs on the plug) then as long as you don't touch the exposed wire you should be fine. if it doesn't have the ground prong (can't imagine that it wouldn't) then it could cause a fault and that could be dangerous. just unplug the heater, tape up the wire with electrical tape, and it should be fine.
The bigger question is why is the casing (jacket insulation?) was burned off the wire. Such as, was the wire undersize, or was there a short in the wire? Sounds like your heater is a potential candidate for a product recall (unless mice chewed through the wire or something like that). I'd get online and search for recalls against your heater, and if nothing comes up, contact the manufacturer (they probably have an 800#). What may come of this for you is a new heater. Don't take a chance of a fire, especially when it comes to something that pulls that much power.
Stop and think about it for a minute dude. Do you really think the heater was manufactured with a burnt wire not connected to anything. The wire got hot and over time burnt off. Either find out where it connects and splice in a new wire or throw the heater away before it burns down your home and maybe you with it! DUCT tape totally sucks for something like this, it will just make the problem worse if anything!
Where is the other end of that exposed wire connected to? Can you just cut it off clean with side cutters (wire cutters)? The wiring in the heater has a high temperature insulation rating but not general purpose duct tape. It will be a fire hazard. If you're going to get a new heater then just remove the bad wire for now.
cut the end off down to the insulation and put a wire nut onto it. every electrical circuit has 2 wires - in and out. what happened to the other end? obviously, u will only get 1/2 the heat unless the bulbs are connected in series, the u will get nothing. I would assume there is a high and low setting - so it will only work on one of them but will always be low.