Override Nest thermostat value with house average temp

Hi,
I have a Philips Hue motion sensor in every room in my house - these also have temperature sensors in.
I’ve taken an average from all the temperature sensors to get an average house temp.

I now want to override my Nest Thermostat temperature value to my average house temp so that my Nest turns the heating on/off based on the average temp and not the one in the living room (where the nest is). Is this possible?

I would like to do this also…

Although I can’t work out how to override the thermostat value, I have worked out how to turn the heating on / off based on the average house temp. Generally speaking when its 20 degrees in my living room (where the Nest is), it’s 18 or 19 on the average house temp sensor. This means that unless I’m in my living room, I get cold. Therefore I have set it up so if the average house temp drops below 20, the Nest turns on to 23 degrees, which I have worked out is high enough to get the average house temp up to 20. If for whatever reason the average house temp gets hotter than 20, I turn the Nest back down to 20. Not perfect but it works quite well for me.

  - platform: template
    sensors:
      average_house_temp:
        friendly_name: 'Average House Temp'
        unit_of_measurement: '°C'
        value_template: >-
          {{ ((float(states.sensor.kitchen_temperature.state) + float(states.sensor.living_room_temperature.state) + float(states.sensor.hall_temperature.state) + float(states.sensor.landing_temperature.state) + float(states.sensor.bedroom_temperature.state) + float(states.sensor.office_temperature.state) + float(states.sensor.bathroom_temperature.state)) / 7) | round(0) }}


  - alias: "Average House Temp control"
    trigger:
      platform: numeric_state
      entity_id: sensor.average_house_temp
      below: '20'
    action:
      - service: climate.set_temperature
        data_template:
          entity_id: climate.living_room
          temperature: '23'
          operation_mode: Heat

  - alias: "Average House Temp control off"
    trigger:
      platform: numeric_state
      entity_id: sensor.average_house_temp
      above: '20'
    action:
      - service: climate.set_temperature
        data_template:
          entity_id: climate.living_room
          temperature: '20'
          operation_mode: Heat
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