Not necessary. Just put HKTKitchen_Average_Temp in your influxdb.persist file (no *). Then the state of the Group will be saved just like any other Item.
You never need to write identical Rules 30+ times. That’s what the Member of rule trigger, triggeringItem implicit variable and Design Pattern: Associated Items is for. You can handle all 30+ Items with one six or so line Rule (only one line of actual code).
rule "do conversion"
when
Member of AverageGroups changed
then
postUpdate(triggeringItem.name+"_PersistItem", triggeringItem.state.toString)
end