By Jane Sutton

MIAMI (Reuters) - Tropical Storm Fay swept into Florida from the Gulf of Mexico and soaked the state on Tuesday while growing strong enough that forecasters said it could become a hurricane before smacking Florida a third time.

Damage was light as Fay blustered diagonally across the peninsula. At 6 p.m. EDT (11 p.m. British time) the storm's centre was over central Florida about 50 miles (85 km) south-southwest of Melbourne, the U.S. National Hurricane centre said.

Tropical storms are powered by warm ocean waters and generally weaken quickly once they move ashore. Fay defied expectations by growing stronger over land.

"In fact, it is stronger than it has ever been so far," the hurricane forecasters noted in their advisory.

Fay's top sustained winds rose to 65 miles per hour (105 km per hour), making it slightly stronger than it was when it passed over the Florida Keys on Monday or when it came back ashore in southwest Florida on Tuesday.

The land in Fay's path was so warm and swampy that "it might not register that it's really land at this point," said Corey Walton, a hurricane support meteorologist at the Miami-based hurricane centre.

The core of the storm was expected to move into the Atlantic Ocean on Wednesday, possibly growing into a hurricane over the warm Gulf Stream current before curving back into north Florida on Thursday. It would become a hurricane if its sustained winds reach 74 mph (119 kph).

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