Cycle Furnace Fan Based on Inside/Outside Temp

True, but you could trigger the rule when any of the temperature inputs change in value:

rule BasementFan
when
  Item outsideTemperature changed or
  Item basementTempSensor changed or
  Item kitchenTempSensor changed
then
  // do this
end

Of course you are also looking for what “do this” is. :smile:

Also, you might want to consider implementing a form of hysteresis to prevent the fan from switching on and off in short cycles.

this post talks about how to actually turn the fan on and off.