yes running without a thermostat is bad. Reason being is because coolant is constantly flowing which doesnt allow the motor to properly warm up, this can result in lack of performance, and running rich, just because were in Florida is not a excuse to not run one. Your ecu has whats called a Warm Up procedure, the ecu dumps more fuel to warm up the motor quickly so that you can get to optimal operating temp. Just so you know a motor performs better in the 195-210*F this helps with combustion because the warmer the fuel is the better it is for atomization which means a better burn which means mo powa. Do a google search for "Wall Wetting"
throw in a new OEM thermostat, do not get a Nismo one as that lowers the temp, you want optimal operating temp.