I now have the same problem with my new Fabia (April 05) as with my old Fabia (April 02). That is, the heater controls have gone haywire. The rotating dial does not work gradually - heat is either on or off. And they sometimes change temperature of their own accord.

I thought this was an old problem that should have been fixed by now. I have not found many posts that mention this problem over recent months. The old posts referring to this suggest it could require a) Vagcom reset, new heater motor unit, or c) new heater control unit.

Anyone had this problem on a relatively new Fabia? If so, what was their fix?

Yep common problem, same cause and effect.

Read codes, reset motors if that doesnt work replace motors.