Heat soak is not likely the problem. I've seen several variants on this:

Electric choke doesn't work (on models that have an electric choke) or is misadjusted. Pop the air cleaner off and watch it following a cold start -- the butterfly at the top of the carb should be completely vertical after two or three minutes.

Choke linkage disconnected (on both electric and manual choke models). The rod that operates the choke butterfly loses its tiny retaining clip and comes loose, so the butterfly stays closed when it shouldn't.

Excessive fuel pressure over-riding the floats. This should be 4 PSI or less. This has to be checked with a gauge.