Re: Savings?
In such a house it would make no sense to have the heat go off when you leave for the day.
Your energy loss is related to the delta T between your outer wall and the atmosphere. Ignoring hypothetically super-insulated houses, even buildings built to any modern building regs will have a clear and measurable heat loss. The thermal inertia of a property is a red herring because that only affects the warm up/cool down times, and has very little bearing on the the rate of heat loss. So you need to minimise the temperature difference OVER TIME. That means insulating to the most economical level, and not leaving the house heated when nobody needs it. Sorry if this doesn't fit your view, but unless you can change the laws of physics, that's how it is.