Thermostat controls about 50% of your utility bill.
It’s NOT true that a furnace or air conditioning works harder to warm or cool the space back to a comfortable temperature after the thermostat has been set back. When your place drops below its normal temperature, it will lose energy more slowly. The lower (or higher in summer) the inside temperature, the slower the energy loss.
So when away, you save more by lowering temps in your home during the winter or raising in the summer, than keeping a constant temperature.