As an ex-trimmer, I can tell you that if a pad overheats and it doesn't work with a thermostat (AFAIK Omegas don't have thermostats), it'll be fooked.
You can buy Weaco (?) pads - it's what we used with no complaints as retro fits - and as said, when the original pad is stuck to the cover, just fit these behind and it'll take a minute or so longer to warm yer arse. They come as a kit for around £70 per seat, IIRC. You obviously won't need the electric wiring, relay and associated gubbins, just connect the wires to the existing loom.
I will say that GM are notorious for fitting seat pad wires where the seat either reclines or folds, so they very often get broken or chafe through and short out, so that's the first place I would look if things aren't right.
Andy is right about hog-rings, but they are cheap as chips from an upholstery suppplier, and cable tiies work just as well.
The worst thing is pulling the cover back on to the seat, as it can be a right stubborn t**t! Don't be afraid to use a silicon spray on the foam to help the covers slip back, slap it into place or pull the crap out of it to do what you want it to do - show it who's boss!!!!!