This one is a puzzle. I think my first suspicion would go to carburation. Does the carburator ever "run over"? How does the choke affect the running when you first start it? Is gas flow sufficient to the carb all the time. Are there any other symptoms?
Is the shaft for the throttle tight in the carburator? Valves also can cause problems on cold engines. If you've burned "bad" gas, deposits can collect on the valve stems and prevent the valves from closing properly. Generally this problem is less evident at idle and more severe at higher rpm's.
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