In Kentucky we are blessed with lots of rain and plenty of mildew so it's a constant battle keeping the boat from mildewing. If you have darkness and dampness you can start mildew, so get everything dry. If you find some mildew starting try spraying Lysol for mildew on it. I always get caught in rain and I never want to store my boat that way. So after I back the boat into the garage, I empty it and get some old towels to absorb most of the water. In some areas like under the console I have used a hair drier. Finally I place a box fan on the bow of the boat and let it blow air over the deck to get it dry. Prop all of the hatches open. I dry off everything before I put it back in the boat.
I haven't had to do this with my boat (yet), but I did it with a car and it worked really well. The windows were left down overnight and it rained, so the carpets got soaked and then mildew started to develop.
I have a small electric forced-air ceramic heater (The Heat Force) that's about 4"Wx4"Dx6"H. I put that inside the car in my unheated garage. With the windows cracked, I ran that heater for a few days and it dried everything right out. I think the heater cost me about $40. Well worth it because I can use it in a variety of places as a space heater. It has a manual/auto switch, fan only/heat switch, a blower fan and dust filter, thermostat (65 to 85 degrees) and a auto-off switch in case it gets knocked over. It's enough of a space heater to heat my office at work when the regular heat is turned off.
If and when my boat gets wet, and its cold outide, I can put this heater in my bilge area and let the warm air circulate below-deck. It will flow out through the various gaps, lids and openings and help dry out the carpet and wood. I could also put my boat cover on, put the heater on the deck and let the warm air dry out the carpet.