Had four flights on QR A320s over Xmas/NYand noted the same. The off switch didn't turn off the heat either, just turned off the screen.
Result was a very warm cabin and many complaints to FAs. Their response was 'It's always like this'. Didn't see any sign they advised the guys in the pointy end and things didn't improve.
Oh, out of four screens two were broken - and still hot.
2 1/2 star service.