Just finished replacing my driver's seat cushion and have some observations and pictures to share. My seat heater was coming on fine but would turn off after 3 min and will not turn on until the car is turned off and on, and a few minutes have passed. I had a broken temperature sensor. I believe if yours comes on and goes off after only a few seconds this is an indication that you have a broken heating element not the sensor. They both require same part and work to replace - just replace the seat cushion with the heater & sensor integrated (assuming the seat not the back is the problem) - part # 52-10-7-388-647 - Seat Cushion Pad Left for driver seat. Cheapest OEM I found was at my local dealer who is selling parts online with local pick up - total cost $170.
https://www.thebmwminipartstore.com/
I used the Youtube video referred on the first page of this thread for instructions - work is not hard - taking the seat off the car is much easier that other seats I've worked on since it is lighter and the lack of B-pillar helps a lot. Taking the cushion out is not hard but annoying and time consuming. I think it's best to get a good cutter and just cut the metal clamps as they will be very hard to reuse. Just get two dozens of small plastic ties - they work very well - this is what the guy in the Youtube video does too. Threading the ties under the seat cushion wire is hard initially but as you progress it becomes easy. Just make sure you orient them so that you'd be able to tighten and cut them as you progress in the assembly process.
To get the seat off the car you need to disconnect the seat power supply - this is very easy but if the car is not completely off it will trigger an airbag warning that needs a special tool to erase. I wasn't worried about this as I do have the tool - I just turned the car off but when the door is open the instrument cluster has the BMW logo on it. After I put the seat back and reconnected everything the airbag warning was triggered and I had to clear it. I believe you'd have to wait for the car to go into sleep or remove the battery to make sure the warning is not triggered if you don't have a tool to clear it.
I peeled the heater off the cushion where the temperature sensor sits on my old cushion just to see where the problem was. I took some pictures that might be helpful if someone wants to fix it rather than buy a new cushion - it seems an easy fix in my case. If I have to do it again I would first try to fix mostly because I like to revive thigs rather than throwing them away. The guy in the Youtube video shows how to measure the resistance of the heaters to diagnose the problem. There are three wires coming out of the plug - brown, green/purple, and black. The green/purple splits into green and gray before it gets into the cushion - the green one goes to the heater, the gray one to the sensor - this picture shows the wires:
https://photos.app.goo.gl/4YQayW368aRC9zBu5
I measured the resistance of the new cushion at the plug between the black and green/purple - it was around 10 kOhms, bad one was zero as the black wire was broken. Here is where I had to peel the heater pad to get to the sensor:
https://photos.app.goo.gl/2TCMmKpKUsyo2chX8
Here is the sensor from underneath the pad - the sensor is still inside the pad - you can see the two yellow wires leading to it:
https://photos.app.goo.gl/vHyxqwGiAT6Mky7RA
And here is where my black wire was broken:
https://photos.app.goo.gl/tmzfJ2sMP1fvwP5f7
This must be a weak spot as you can see that the gray wire has the insulation broken too. It seems it would be easy to replace these with new pieces of wire.
Hope this helps others to diagnose and fix these problems. Cheers.