I installed a Honeywell RTH6350 Programmable Thermostat a week ago and everything has been working fine. Today, the display shows that the Heat is On and the fan automatic. Nothing is running. When I put the fan to ON instead of automatic - nothing. I flipped the circuit breaker and checked my wiring. Nothing has changed. What else could it be? Cooling does not work either.
Honeywell RTH6350

Sounds like you have lost power to furnace,1st check breaker with meter,, it could be on but no power coming out,, also the transformer may have blowed. Check for power going in and low voltage 24-28 volts coming out on other side,, it might help to tell us what kind of furnace,, electric or gas

,, get back to us with what you have found

Transformer may even have a fuse.

Had to call the "experts". Put in a new transformer. Ran all of 4 hours and died. Waiting for another in the morning. Is this normal??

Nope, something is taking out your transformers. I would suggest installing a fuse on the low voltage side of the transforer. Much easier and cheaper to replace a fuse than a trans. Also, during touble shooting, it may take a few fuses to get things tested correctly, vs a few transformers to get it figured out. I can see one transformer going bad, but a new one right away? not likely unless there is a problem. Hope they get it figured out. Take care.

If you have no shorts on your thermostat wiring, or your low voltage wiring out to The Outside Compressor, then maybe a relay or Contactor has shorted windings, drawing more current.
Could be the transformer is too small. Resistance or current test on any relay or contactor coils may show the culprit.