I would not try to put the heat on and try to dry it your self i would let the dealer do it and do it quick.
the drains for my soft top cloged, and only about 2 -3 feet of pasanger side carpet under the seat got soaked. I pulled the carpet up after 3 days of not knowing and black mold was growing and it did not dry out after 4days of carpet out with a blowdryer and venting it out all day, so get it done right.