Nest is not as smart as advertised, and I should not have bought. Here is why:

1st : Nest doesn't know how much you pay for electricity/fuel...

2nd : Nest almost emptied my fuel tank last fall : I add it filled in septemper and refilled in in January. With the old thermostat, a tank was enough for the whole year. The reason : when I used a schedule to lower the temp during the day, Nest Auto-Learning learned it was faster to reheat using the oil, even in the summer.

I think I will rewire the furnace / thermopump so that Nest only tells to heat, and then my solution will deal with using the oil or the thermo pump or the baseboard heaters.