Once it blows warm, if you shut it off for say 10 minutes and leave the blower running... when you turn it back on does it blow cold again?
That could be an indication that the evaporator core is freezing up.. I would normally associate that with low freon (which when low, only wets part of the evaporator core.. that portion only, freezes over and, and hot air will be passing thru the upper part of the core that's not being wetted by liquid freon). What happens is the cold temperatures on the lower part of the expansion core due to the freeze up is sensed by the thermostaticly controlled expansion valve, and it starts limiting the cooling capacity accordingly.
Florida can be very humid and unless everything is tip top, evaporator core freeze ups can be common... Even in North Carolina, at times I have to run with the air intake on the recirculate position to avoid freeze ups due to the high humidity.
Next, when it goes warm, have you opened the hood and looked at the compressor to confirm that the compressor clutch is still engaged? There are both low and high freon pressure limit switches in Toyota A/C systems that will shut the compressor off if pressures go either too high (overcharged system) or too low (undercharged system).
If the right amount of freon is in fact in the system, then the expansion valve (which has it's own thermostat as mentioned above, might be a problem.. This is expensive enough and difficult enough to replace that, getting a top notch A/C guy to confirm would be in order..
A typical preformance test of an A/C system is to run the system at fast idle, A/C air set on outside air intake, fan at high setting and vehicle doors open so interior doesn't cool down enough for the thermonstat to throttle the system. Then put one A/C test thermometer in the outside cowl air intake and the other in the interior A/C outlet duct.. Systems working correctly will produce a 20 deg F or better temperature drop.
