I don't think swapping sensors would be feasible, but you could just let the BMW one in place and use the one from the new mat.

But, what you need to know is if the BMW sensor will lower in resistance as heat rises, like the EBay one.
Take a measurement cold, then heat, then another measurement like you did with the EBay one.

Another possibility could be the electronic module that has cold solder joints. As the air temperature changes, the PCB will expand and retract, and if the solder joint on one critical component is cracked, the component may loose electric contact.

I don't remember if the connectors are the same for the L and R seats, but swapping seats (without bolting them) could help know if the problem comes from the seat or the control module.

pics?
 

Anyone have a copy of the pics (links are broken)...

Great , so does this mean the seat pad/cushion and back are interchangeable from driver side to passenger? I want to switch my leather seats out, driver is beat, passenger is like new. OH, no heaters, but I would love to put this Dorman in. Thanks

I also have the dreaded heated seat problem. Turbo Bimmer mentioned the following in the original post:

"The BMW heat pad is sewed to the leather, but on the edges only."

How hard would it be to unstitch the defective heat pad from the leather cover, then sew a new one in its place?

I've found a lower cushion with a working heat pad, but it's in the wrong color. My upholstery shop may not be comfortable with doing the electrical work but may be able to create a working cushion by combining the working heat pad with the original cushion. Or maybe just die to working cushion to match...

Thanks for the help!