The fans on your model could either by controlled by the traditional switch (Like the Sierra) or by the ECU, in any case it's most likely it has dual speed fans and so low speed and high speed there are usually two relays as such. Have you checked the alternator UNDER load?

If fans are ECU controlled which I think they will be tbh and it's gets that flat it may be it powers them on when restored, if it's only doing it when power is restored I would say certainly.

If it's going flat when left then either something is draining it (Check the boot light as said) or the battery can not hold a charge, despite it being new.

You wan't to check the battery voltage both when the battery is charged and when it's flat to see what state it's in.

EDIT: To add it's worth doing a draw to to see how much power is being pulled from the battery with everything is switched off.

Martin