Having fun with Temperature stratification

Just putting info out there - We've all been taught since elementary school that hot air rises. I learned today that warm air can be 7% lighter... wow! that's substantial!
I have 12 temp sensors throughout my environment. They all have been tuned for accuracy (using a +- .1 RF gun sensor). My sensors are all over the place - some in ceiling corners, some on top of book cases, some on desks... and where I have the sensor has a direct correlation to the reported values I get.
Averaging temperatures is actually not really very accurate at all! Why? because of the aforementioned height of the sensor itself. In my case, the difference between the ceiling and the floor is a whopping 12 degree's.
I live in Portland, OR - so we get decent cold during the winter. I'm especially susceptible to cold floors. While the house temperature is balmy, my feet are freezing. Especially in my office where the floor and my feet are near an outside wall, that has venting under the house. Currently the room is 72 but the floor is 64 degree's.
I think that there must be a mathematical way to weight the values based on the stratification. Instead of just averaging sensors, each sensor needs a multiplier to give it weighting so that the overall value is more apt to account for the cold floor.
I know what your thinking. Just put a floor sensor by my feet and be done with it! But the bedroom also has this problem too. As well. I DO have a floor heater in my office - and I intend to automate it. (I've ordered temp sensors - I have extra sensors with motion and temp like a hue or Smarthing but it'd chew batteries at my feet from all the motion commotion!)
Has anyone ever seen any app that considers Stratification?

I haven’t seen any apps that allow averaging several temperature sensors for the set point. The closest thing I can think of is an Ecobee with their remote sensors. It is focused on managing the temperature in multiple rooms, but you might be able to adapt it to your situation. You could also creat some rules in RM to accomplish this with multiple temperature sensors.

Do remember that if you average sensors at different elevations you will effectively be applying an offset to your normal set point. You may have warmer feet, but the rest of your body may feel like it’s on an equatorial island. You can test this and accomplish your goal more easily by changing the set point you use without adding the complexity of averaging multiple sensors.

You could also try creating a rule to turn the fan on for five minutes every twenty minutes even if it doesn’t need to heat the air. This will help reduce the air stratification.

If you want to fix the problem you should look at floor/foundation insulation, baseboard heaters, or underfloor heating. I know these are a lot more expensive, but they will give you better overall comfort.

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great feedback @wayne.pirtle ! I will mention I've actually seen and played with temp averaging apps (I believe Average Plus from @bptworld is one, and I can't recall of the top of my head another app I did try recently specifically for thermostats - I think it was designed for multiple thermo's but ... please don't quote me!).
Speaking yesterday to another HA afficienado - we both agreed there is a no return on investment if I take this too far. I've now put a sensor on the floor, and am using a smart outlet controlled under-desk floor heater - viola. problem solved for $9 (I already had the heater).
Your suggestion of circulation is brilliant. I recently rewired my thermostat with a 5 wire which in turn gave me a feature I didn't have before - the ability to turn on the furnace fan without heat. This in turn is highly useful to move and stir the air and I'm now accounting for your suggestion in my design! I have a terrible tendency to overthink - and often solve with hardware when software will do just fine! Danka.

You’re welcome @jshimota I learned some lessons about over thinking solutions early in my career as an engineer. I still have a tendency to over think things, but most of the time I realize it and may still choose to implement the over engineered solution just for fun.

Let me know if you have any other questions.