Mine also has 2 ribbons. And they do have heating in them but that is controlled based on the outdoor temperature. They're should be a purple and white connector. I swapped the guts from one mirror into mine because the motor control weren't working and the mirrors were moving on their own.
The covers should swap over, but I don't know about convertible mirrors vs non.
'04 330i ZHP sedan | Mystic blue | Alcantara | 6MT | 111k
'98 740il | Schwartz 2 | Sandbeige | 5AT | 238k | lowered on Bilsteins w/ B&G springs
'00 540i sport | Titanium silver | Black | 5AT | 120k
'85 Mustang GT convertible | Medium charcoal metallic | Gray | 5MT | 215k | one owner, all original