Thanks for your advise bbf, since it was factory installed I'll have it verified with my next service in early april. Even if I go right now the night temprature is no longer going as low as it should to reproduce the problem.
I don't know if this could be logical but the thing that I've notice is that if it's to cold to start up the computer decide to turn off all equipement that take to much energy from the battery to be able to start the engine but the computer doesn't turn back on what it has turn off.