Most heater failures is a broken element in the seat bottom. The element is a thin wire that loops back and forth in the heating element pad.
In my case the fix was easier than most because I replaced the seat leather and pulled the heater off the old leather in the summer. Therefore it isn't sewn to the leather like most would be. I prefer to take the seat out of the car. Disconnect the black 4 wire connector heading into the lower seat cushion. This will allow slack for you to work. Then you can unhook the J channel plastic holding the bottom seat cover and use your hand to slide in and pull the velcro holding the leather to the cushion apart. With the leather up and still mostly on the seat you can work.
The white patch is what the factory puts on originally to hold the wiring with some hot glue.

Looking at the heating pad we see two burn marks in it. When I fixed this last week, there was only one mark.

Fixing one of these near the wiring (which is where many of the breaks frequently occur) is rather easy. Lifting up the wire, there was an obvious weak spot. That's where it broke.

Being that I deal with thin buss wire like this for other things, I know that dragging a razor over it (lengthwise with the wire) is about the only way to get the coating off w/o breaking the wire further. Here's the spare piece as I was unable to click a picture while doing the one on the heater.

Then rewrap it on the regular wire coming in and solder. Test with a multimeter for continuity.

Add hot glue to hold things from flexing at the solder joint, then tested again.

I put GM's little sticky patch back on

Then a new piece of super de duper tape (aka the same tape they use to fix a bus seat)

Reinstalled the heater and tested it out. My butt is warm again and that's a happy thing in the cold weather.