Mmmmmmm ............. uninsulated solid stone walls ........ well heated. I wouldn't like to start an argument, but you'll be the one with the heating bills.
In Building, as with everything else, there are many, many solutions available. Heatstore versus rapid warm-up? As I mentioned above, rapid warm-up involves plenty of internal insulation, so you only need to heat the air, not the building. Using the stone mass of the building to store heat, say from centralheating coming on for a couple of hours in the morning, would be fine. In the evening some of that heat would still be radiating from the warm walls. The trouble is, a great deal of the heat plus any you apply in the evening, goes to waste through the uninsulated walls.
The way around that would be to put the insulation on the OUTSIDE of the building.
I've done that before, but only when the external render was due to be replaced anyway.
Project Managers and Structural Engineers ........... I know, I know........... how can I put this diplomatically? .............. They can be a tad "precious" about a project......... stating their preferences maybe a little too dogmatically. There are many solutions. It should be remembered that the whole point of the job is to give the customer the service and the product that the Customer wants.