With heat pumps, the energy required to heat or cool the air is nonlinear, with larger differences costing increasingly more. This is based on the temperature

With heat pumps, the energy required to heat or cool the air is nonlinear, with larger differences costing increasingly more. This is based on the temperature difference between the air intake and output within the house. This only matters for heat pumps with a variable-speed compressor, which can reduce the temperature difference, to save energy. These are often advertised with "inverter" in the name or description. The practical effect of this, is that if you have a heat pump with a variable-speed compressor, heating or cooling your home quickly costs significantly more than doing so slowly, so you are best off leaving the thermostat at a constant temperature, unless there is a significant price change in energy, throughout the day.