I fly LGA-FLL a few times a year, most recently a couple of weeks ago, when I was in the same situation. Layers, as others have posted, is always the way to go. I started out in NYC in jeans, a tee shirt and a wool sweater. Got to Florida, off with the sweater. (And since I had room in my suitcase, I threw my winter coat in there once I got into the terminal - one less thing to deal with at security).