AVG Temp of last 12h

Good question, i think it does only work in rules or scripts.

Create an extra Temp_Outside_Avrg Number Item and create a simple rule:

import org.openhab.core.library.types.*
import org.openhab.model.script.actions.*
import java.util.Calendar
import java.util.Date
import java.util.TimeZone
import java.text.SimpleDateFormat

rule "Temperature Average"
when
    Item Temp_Outside received update
then
    Temp_Outside_Avrg.postUpdate(Temp_Outside.averageSince(now.minusHours(6)))
end

Something like that should work.