I had this exact problem a year ago and then i got burnt by the seat, badly. I got my seat bottom replaced for free. you cn not replace just a wire. you need to buy a new seat bottom which has the wire sewn into the leather. Thank god I got it replaced for free.

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I swear, my cars are like a girlfriend.
Sometimes its a rough ride, sometimes its smooth motorin'.
Sometimes she doesnt like how i treat her and sometimes i dont like how she behaves.
BUT at the end of the day, she loves it when I am inside her.

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'91 850i
'05 X5 4.4i
'09 Clubman S