Lived and brewed in Clearwater FL and own two cool brewing bags. They work great and with one or 2 gallon jugs of ice you can keep the fermenter in the mid to low 60's easily. Best investment and improvement I have made in my beer.
You would need to get a temp controller for the fridge. Good chance that is more expensive than you would want to spend. Around $75. If you keep it around 68 it should be ok.