Re: IofT
You'd also need to take into account how air at different temperatures could move among different rooms and floors unless doors or the like don't stop it properly, otherwise you may end up to spend more than you thought.
And sure, to gain the most saves a thermostat should start heating at least half an hour/an hour or so before you need to use a room (depending on the heating tehcnology and building characteristics), and may stop earlier than you leave - but it has to be able to know (or predict it well enough).