You can insulate to exclude draughts from windows and doors, and line the roof / roof space to prevent heat escaping upwards. Stone walls are *meant* to breathe. Thick stone walls work like a heat sink. Get them properly dry and warm, then aim to maintain the temperature. Allowing the temperature to fluctuate is not so good - but the stone walls will help with that themselves, once they are properly warm and dry. Like huge storage radiators!
We have an air source heat pump and a heat recovery system in our old stone farmhouse. The walls are not insulated but we fitted new triple glazed windows and all the doors are draughtproof. The ground floor is communal space - a bathroom, a larder, large kitchen, large dining room - and there are two flats above. The flat in the roof was recently converted and is well-insulated, the middle flat is older but both ceilings/floors are fire-proofed and heat- and noise-insulated. All levels of the house can be kept nicely comfortable with the air source unless it gets very cold - which for us in North Cornwall means below 5C, and / or blowing a hoolie with rain or sleet from the north or east. The dining room and the middle flat have wood burners which are used when needed, which mostly they are not. The top flat has underfloor and tops up with an electric heater if needed, which is not very often - and she is Swiss and likes it *very* hot, like 21C+.
Of course we cook in our communal kitchen maybe 4 or 5 times a week, and all that heat gets recovered by the heat recovery system, so that helps too.
Big thick radiators for heat pumps. (Same for ground source, which we have in 6 of the houses.) IMO, it works best having the water temp much as it comes out of the system, and maintaining a low constant heat so that the spaces don't go hot - cold - hot. If sitting down for long periods, wear winter woollies, use a hot water bottle and a shawl if you need, rather than heating the entire space to 20C! And go take the dog for a walk or chop some wood or something if you get cold; the house will feel toasty when you get back in!