FPUS42 KJAX 200627 City Forecast for Gainesville, FL Issued Monday morning - May 20, 2013 .Monday... Thunderstorm, high 85, 50% chance of precipitation. .Monday night... Low 65, 30% chance of precipitation. .Tuesday... Partly cloudy, high 87, 30% chance of precipitation. .Tuesday night... Low 66. .Wednesday... High 87.