Steffo,
I've been running dust covers on my Jayco hawk for 4 and a half years and have done some miles.
I have never had a problem even with it shut up, fridge running on a hot day (think 45 degree's - NT) for over nine hours and other than the bench top being "mildly" warm to touch, not a problem.
It doesn't help with the fridge cooling and chews battery power, but while your driving it doesn't matter.
I however always remove them when I stop. and never ever ever forget the door vent -( gas regs, death etc etc)
Brian