A burnt wire does not get burnt on its own - it either takes too much current and gets hot because of over curent for its size - or it gets burnt from radiated heat.
If you put a new wire in it may burn up again - it would be good for you to try to discover why the wire is burnt. An overcurrent situation may well have blown a fuse before the wire burnt - that's why we have fuses. If it's radiated heat then it either happened quickly or over an extended period. If it happened quickly then a new wire will burn up quickly too - whatever it was that caused it will still be causing the same thing to happen to any new wire.
If the burning happened over an extended time it may be just down to poor routing of the wire close to a source of heat. It may be a good idea to route any replacement wire away from the heat source.
As for disconnecting the old wire and reconnecting a new wire much will depend on the terminations at each end - where does the wire come from and go to. What function does the wire have etc. etc.
Nobody here can see your burnt wire and can't see the terminations - the difficult bit to say is - given that you need to ask such a basic question it is strongly suggestive that you do not have the skills or confidence to make this repair yourself. You may do better to call in an engineer.
Good luck...take care...
Peccavi
October 2009
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix tumble dryers.