A small, portable electric heater (set on "low") might do it.

Here in Canada, our car carpets get wet from snow/ice on boots, and stay that way until it thaws out in the spring. Or on a longish car trip the in-car heater/blower may also dry them out a little.

There should not be water puddling under the carpet -- there are supposed to be drain holes under there. Perhaps they're clogged?

EDIT: A wet/dry "shop vac" could be used to suck the loose water out of it.


Cheers