I dont know anything about those auto chokes. But you need to remember that a cold engine needs more fuel. If the choke was at fualt after warmed up the engine would die from too much fuel, not race or increase idle. Increasing idle or "racing" are indicative of a lean condition. Lean means too much air or not enough fuel.
Look elsewhere if it starts fine because the auto choke is most likely working as it should. (edited)