Is there a temperature below which a conventional heating system is cheaper to run than a heat pump?

Yes. Using 2022 energy prices, oil is more expensive than heat pumps above negative 1F and propane is more expensive above negative 11F. Switching to oil or propane below these temperatures and then failing to switch back to heat pumps exactly when temperatures exceed these points could end up costing more. Therefore, we recommend against switching back and forth.

Assumptions: Oil at $3.86/gal, 87% combustion efficiency, and 80% distribution efficiency. Propane at $3.43/gal, 90% AFUE, and 80% distribution efficiency. Electricity at 22 cents/kwh, heat pump COP=2.93, and 100% distribution efficiency. 80MMbtu/yr heating load.