Heat pump, 13-14 year old Rheem system. 3 or 4 ton unit (don't remember exactly, but I think it is a 3 ton). Air handler mounted on ceiling in garage.

I live in Florida where heat is used about 3 weeks out of the year. Recently, we replaced the low voltage transformer in the air handler when it stopped working. I noted that it stopped working around the same time that we needed the heat for a couple of days. Since then we had been using A/C until a recent cool spell swept through that required heat to take the chill out of the air. Upon switching the system over to heat again, the transformer died again. Now, the transformer itself is cheap enough, but I would really like to find out why the system keeps frying the transformer so I can get to the bottom of the real problem.

Does anyone have any thoughts on where I need to begin?

(this is the transformer that connects to the 24V line that I believe goes to the thermostat)

Simple to do.
You need to trace your heat circuit from the thermostat to the furnace and find the short circuit.Since it does not do this in the A/C mode at least that part does not need to be checked.
Many times a wire will rub and short circuit.
To do this you will probably need a meter to check the thermostat cable.
I would also put a inline fuse in the transformer circuit so as you are testing and if you do this you will save yourself the purchase of another transformer since the fuse will blow and not the transformer.

Won't have the opportunity to check this until the weekend, but thankfully, we won't need the heat.

Also, thanks for the quick response hvac1000.

Post back with your results