There are many factors at play in drying out a crawl, warm outside air being one of them. Most crawls that I have seen that have water problems are from bulk water intrusion, i.e. a disconnected sewer pipe or high water table, especially when that water impacts the wood members of the house.
So what to do? First, follow the international residential code and ventilate your crawl (1 sq ft ventilation per 150 sq ft of crawl, or 1 sq ft per 1500 sq ft of crawl if you have a vapor barrier). Next, physically inspect your crawl. If there is standing water present, deal with the source. If there is no standing water, then leave the ventilation alone.