True?: Heat rises, so you can put thermostat lower upstairs

Heat does go up in a house mainly through the staircase. And this would mean that if all heating elements are of equal power, then the top floor would be warmer.
As nascentO2 pointed above there are many factors that can influence this, one more being a staircase door or curtain (not usual).

Placing the thermostat lower will mean it senses a lower temperature and thus heat the house more. This is not economical at all, it is just like setting a higher temperature on the thermostat itself. For true economy, set your heating elements for more radiative power downstairs to compensate for the updraft, by using a thermometer in both floors and comparing. Basically uniforming temperature is both comfortable and more efficient as in a well isolated house.

Edit: I forgot to mention that, the reason why a uniform temperature is better than a gradient. Basically the two hot/cold non-uniform parts add to more energy being radiated away as emissive power is not linearly dependent on temperatue, rather T⁴, so the hot part loses a lot more energy than the cold part would save, compared to a uniform mean.

 

The simple answer to the OP is that the thermostat will keep itself at the required temperature. IF it is sited at the top of the house, then it will require less energy from the system to keep it at a given temperature. Downstairs will be cooler. If sited downstairs, the Upstairs will be warmer and you will need more total energy input.
You can have as complicated an answer as you want, beyond that basic one and you would need to specify what the actual situation is.

 

True, it is small compared to convection and conduction, yet it is what makes the difference in the heat loss of a house with a temperature gradient vs. a house with a uniform mean temperature, given the same heating power input. For the big outer surface of a house it should not be negligible.

I was hasty in my statement, thank you for completing it.

 

My calculated radiative loss for this winter is 15% of my whole heating bill. By using 0.5 for emissivity (as I cannot really know the emissivity of a brick concrete wall I cut the error in half) , a 2 degree Kelvin difference between outside temp and outside wall temp (both measured), and dividing by my heating bill for a month converted in W (so a mean). I know it is not used in heat loss calculation but I cannot call it negligible.
And this tells me I need to insulate my outside walls to reduce their overall outside temperature.

 

Is the temperature of the outside wall 2k hotter than ambient due to losses from within the house or the sun heating the walls?

 

As for the OP. I think Russ has the answer. Turning down the upstairs thermostat makes no difference IF the room is already above the set temperature because it's heated by another source (eg from downstairs).

 

1. Complete data: Area 56 m^2, emissivity 0.5 (0.8 would be closer from what I've found), Twall 273, Tambient 271 . Power loss 256W (not a lot), Monthly power consumption 1735.764 W.
2. measured the temperature at 22:00 after a really cloudy miserable day (w/o precipitation). Wall was straightforward measurement 0(+-0.1). Ambient was even easier, took a shot at the ground and night sky (cloudy). Both had that -2 Celsius (+-0.1). Measured with a cheap temperature laser gun (don't remember the maker).
3. It was winter so the wall is hotter than outside ambient, and my walls are completely uninsulated brick with a shot of concrete. I usually talk about outward heat loss, so from the house (apartment in my case) to outside ambient, as it is true loss, inside transfer is not a loss in my opinion, unless it affects outside loss. As such I really mean the outside surface of my house had 0 Celsius and the outside ambient had -2. While it should be the same on the inside the surface calculation + conductance through heat sinks is too much a bother.
I really doubt that you can sense a 3 Kelvin night-sky temperature considering we have 10 tonnes of atmosphere above us much hotter than space. When pointing at a clear sky it was colder than usual but only by a few degrees (remembrance).

Convection is easy to estimate for the inside but given varying wind makes it slightly complex for the outside. And while nobody bothers with radiative power+conductance+convection, I'm sure they still pump the convection value by a factor of 1.2 without knowing why (one of those constants).

 

I like to transform everything to simple W or J (rarely). So 256 is in simple W. The 1736 W or monthly average heating power, came out of a close to 1.2 MWh that my gas bill shows of course divided by seconds (I did ignore the electric, as it contributes only lightly to the monthly average power). For some reason they decided for themselves to bill us according to gas quality in MWh/cub meter although they measure volume, just to add to the general confusion that is the gas bill and it's pricing.

I don't know my R value, And I'm not sure how insulating the brick in the wall is ( it could be of Porotherm type which insulates better, but I just don't know). And I do share walls with lots of neighbors, but they are not this giving. I do agree something can be off as I have no values for wind or humidity.
Still my heater is 24 kW, yet at a 6.3 kW it should work at full for 8 hours per day (which it doesn't), my 1.7kW seems fine to how much it is in heating mode.

Btw had the chance to measure the nightsky a few nights ago, a chilling -38 C, when it was only -5 outside ambient, after a moderate snowstorm.

 

In my opinion radiatiative losses must be important, although surely smaller that convective losses. That's why temperatures drop considerably faster on clear nights compared to cloudy nights.

 

Odd indeed. While dividing by the hours would make a lot of sense. I first transformed into Joules the converted into W (which implies an unnecessary multiplication and subsequent division by 3600, yet i like to see both values in my excel table). The 256 W is the radiative power of a body of the given surface, emissivity and temperature difference, at least what i came up with.