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I would say you have a carb issue... more than likely
its running lean on the warm up.. I will guess its
running at a lower than normal rpm when cold(just
staying running) and would be a choke issue

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I agree on the choke issue but I have seen the opposite with chokes, there adjusted to rich, when their adjusted lean they die and won't stay running, at least it is that way west of the big muddy OP, you say you changed the carb or it doesn't have the original carb. on it still look at the choke adjustment, even if it has the original carb. on it look at the choke adjustment When cold you should see the choke plate almost closed to the divider in between the front and back barrel, it should not be closed all the way and tight Look at it with the air cleaner off, open the throttle about a 1/4 of the way to full throttle and let it close, look at the choke plate then . Start the car up and see if the choke pull off is pulling the choke blade open some when running or if it is not doing anything Let us know what you find