your home is probably not suitable for cavity insulation. If the walls are plasterboard you could, if you feel like it, have it relined with Kingspan insulating plasterboard which has a high-efficiency rigid foam slab bonded to it, and can be skimmed over with plaster. The 1980's method was to batten out the walls and put mineral wool between the battens, then nail plasterboard over, which is not as good, but adequate.
A barn conversion is rather non-standard and if there are gaps between the skins I would hesitate to inject expanding foam as it may fall or expand into a gap that is supposed to breathe.
Instead of rags or newspaper, you could stuff the gaps with loft insulating quilt. You can get a white one, at twice the normal price, which is made of recycled soft drinks bottles, plastic not glass, and sheds no fibres. Otherwise I would use the mineral wool treated with Ecose to prevent it shedding dust or fibres, it is made by Knauf but sold under various brands. Look for the name Ecose on the wrapper, I wouldn't use anything else now as I am sensitive to dust. It is brown, not yellow and feels soft and silky. Having stuffed the gap you can use Silicone sealant on top, which will stick to clean dust-free surfaces, esecially if newly painted, and will squash and stretch a bit without cracking. Acrylic filler and decorators caulk are much cheaper and easier to apply neatly, but will crack with expansion and contraction.
Silicone is available in numerous colours but does not take paint well.
Is the roof very well insulated?
and...
heat loss is directly proportional to time x temperature difference. So if outside is 0C, heating the inside to 20C will lose twice as much heat as heating it to 10C. Keeping it at 20C for 24 hours will lose twice as much heat than as 12 hours.
There will be a delay in temperature rise when you turn the heating on, just as there is a delay in temperaturte drop when you turn it off, which will depend on the specific heat and mass of what's inside the heated envelope. In typical houses, you have the timer switch the heating on half an hour before you get up, or come home; and switch it off half an hour before you go to bed or come home. A modern house will only drop by a few degrees in a few hours, it will not get frosty inside.
Heating an empty house will make it more comfortable, but will certainly lose more energy and cost more.
Think of keeping a kettle simmering on the stove all day rather than boiling it each time you want to make tea. It will be losing heat all day.