Does your original thermostat have an Emergency Heat switch on it?
The white wire is usually used for the AUX heat and the Black wire for emergency heat. They sometimes wire it like you have when there is no emergency heat switch on the thermostat.
If you look in the air handler/furnace there will either be a control board with a terminal block or a bunch of wires with wire nuts that the thermostat cable connects to. If it is a terminal block, you can look and see if the black wire is connected to anything. If it is, then post what it's terminated to. If it isn't connected, then you can just leave it disconnected on the thermostat side.
Post what you find here
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