I tried both ways. It turns our that for me it is best to turn the heather off when it is not needed. I use on-demand gas water heather for hot water and for radiators, I work for 8 hours, so there is noone home from 7 am to 5 pm, we sleep with the windows slightly open, I have 2 small children so we keep it warm when we're home, the building has a good insulation, good windows etc, etc and even if the temperatuire outside is -20° C it almost never drops below 17 inside. The building is in fact built as a low energy house although it doesn't have any certificates. For me the bills for gas are slightly lower if I turn the heather off during night and when there is nobody home.