Well, I will attempt to assist on the electrical. Anything need clarifying please ask!
What year are these seats?
I found some info here
BMW Heated seats
With 24V setup, you would need 2 heaters in series, only one grounded...
24VDC+----(12V heater)-----(12Vheater)-----0VD(GND)
This would work well if both seat and back were separate heaters as they could be wired like this. NOTE that BOTH heaters would always turn on and off together. You can not run just one of the 12Vheaters off your 24V supply, always 2.
Temp sensor is likely just a restive bi-metalic probe. Its resistance will vary based on temperature and the resistance curve will likely fit into a standard curve (ie type K or J thermocouple). You probably don't need to worry about this.
PWM is Pulse Width Modulation. I think we are all familiar with the typical AC sine wave and what it looks like.... PWM is a SQUARE wave, where the voltage near instantaneously rises to say 5V, stays on for a certain period of time, and then drops to 0V for a certain period of time. The ON time vs the OFF time is what is referred to the pulse width. Generally much faster frequency too, in KiloHz ranges.
So the heaters on your seats are likely just after a transistor or triac that acts as an electrical switch and this switch is enabled with the PWM signal is ON. This wire is likely smaller as little current travels through it, it simply enables current flow through the heater circuit. When connected to the PWM signal, the heat produced is directly proportional to the width of the ON vs OFF time of the pulse.
I am guessing that if the PWM wire in the seats was jumpered on (100% PWM duty cycle) the heat would be on full and you could manually flick the switch when your heiny is too hot/cold.
Other than that you *may* need a small micro-controller to get proper control of the seats. Maybe this is part of the dash switch assembly in the BMW and can be purchased from a wrecker? Or you will need a small arduino (or similar micro controller) to generate the PWM signal.
Sounds like a fun project!
EDIT : Lots more info here
DIY: Non-Heated to Heated Seat Retrofit!! Lots of Pics!!! - E46Fanatics