In nearly every webpage that I read on the topic, it is recommended to not let a house cool down over the day (even if nobody is there), but to instead keep a constant temperature. This is reasoned by the sentence "It takes more energy to heat up the house again, than you would save by not heating it for a certain amount of time".
To me, this is unintuitive behaviour, to say the least. The house (or the flat) loses energy to the surrounding buildings / air / ground by conduction, by air movement, and by radiation. In any of those heat-transfer-mechanisms, the energy loss will increase with increasing temperature of the house.
So my question is: What am I missing? It can't be that I'm right and any plumber / heating technician is wrong. Could the problem of overshooting temperature during the heating explain this? If so - why? The energy that is too mutch stays in the house.
To keep the house at a constant temperature, I have to balance out the energy loss. To reheat the house, I have to deposit the energy in the house that was lost during the cooling. Because of the mentioned temperature dependence of the energy loss, reheating to temperature $T$ should take less energy than keeping the temperature, because less energy was lost.
I'm well aware that houses shouldn't not cool down too much (because of freezing pipes, moisture in the walls, mold, etc ...). This should not be the topic of the question. In case it should matter, I live in germany.