FPUS42 KJAX 291455 City Forecast for Gainesville, FL Issued Tuesday morning - Nov 29, 2016 .Tuesday... Partly cloudy, high 85, 10% chance of precipitation. .Tuesday night... Low 64, 10% chance of precipitation. .Wednesday... Partly cloudy, high 83, 10% chance of precipitation. .Wednesday night... Low 66. .Thursday... High 73.