A multizone smart solution would probably be a really good fit for you. Large house not all rooms being used - pretty much where they excel over a standard theromstat and programmer.
If you ever do get one look beyond the single Zone smart thermostat - if you have a a pretty static routine and programme it well you won't use it much. But a mutlizone like Honeywell , Tado would really come into play heating the main rooms you use , when you need them etc.