Your thermostat controls your HVAC system. That goes for your AC just as much as it does your heater. Since your heater can’t actually detect the temperature on its own, it relies on the reading from the thermostat and its signals to know when it should turn on or off.
You need heating repair in Sarasota right now–that much is clear. But now let’s clarify if the problem is coming from your heater, or if it’s the thermostat that’s making it look that way.