2005 Volkswagen Golf when hot problem restarting car

Any codes logged ,also could be throttle /air flap sticking ,also engine temp,sensor check or replace if associated code logged.

Worth checking the cam and crank sensors also .

Try heating up the steering column control module which is coupled with the ignition switch with a hair dryer. Have your engine running and lights on etc. This module does not like it hot. See if it cuts out. Worth a try