From a thermal energy perspective this simply isn't possible.
However, some systems do lead to this because of flaws in the the implementation. My ground heat pump, for instance, has a backup electric heat system that it will automatically, and unavoidably, utilize if it hasn't reached the target temperature within a set, relatively short period of time. So in my very well insulated home I do indeed see significant cost increases if I do temperature setbacks, as the recovery period sees more expensive/less efficient electric heat kick in, versus just incrementally using the heat pump through the day. Some fuel-based systems go to a less efficient high-heat stage in the same sort of situation.
However, some systems do lead to this because of flaws in the the implementation. My ground heat pump, for instance, has a backup electric heat system that it will automatically, and unavoidably, utilize if it hasn't reached the target temperature within a set, relatively short period of time. So in my very well insulated home I do indeed see significant cost increases if I do temperature setbacks, as the recovery period sees more expensive/less efficient electric heat kick in, versus just incrementally using the heat pump through the day. Some fuel-based systems go to a less efficient high-heat stage in the same sort of situation.