We also live in a very old rambling stone house Mamie (from 1587) 90cm thick limestone walls + plaster, and insulation and cladding for some rooms. We have a belter of a large granit wood burner in the kitchen which keeps the whole of downstairs warm, and when it gets too hot, we open the kitchen door so heat can escape up. If you don't have any doors- then you will lose all the heat up. Not sure about the configuration of your house, but a friend of ours got a lined sail (as in sailing ...) made to fit in the gap where the stairs are to stop this from happening- maybe something to think about?
We live in the mountains, at 950m (about 3600ft)- so our Summers are warm during the day, but always cooler at night- and we just close the wooden shuttters and leave windows wide opened- if it is too hot still- we open the door to the barn at the back to create air movement. Those big stone walls seem to keep the house warm in winter, and cool in Summer.