sounds like one of two things,
fuel enrichener aka (auto choke) is not closing. this is the part of the carb that has the wires going to it. it provides extra fuel while cold then closes that feed off when warm.
someone also might have adjusted the float to compensate for dirty pilot/ part throttle jet so it would hold idle when cold by drawing off the main circuit with what would normally be a too high of an idle position.
TBH, either or these issues or anything carb related with these, a cheap ebay carb is a quick and inexpensive way to get back running vs the time it takes cleaning and testing 3-4 times to resolve the problem. i don't even hesitate replacing them any more.
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