If you are still using the original "hot air" choke verify that there is adequate vacuum at the line coming off the choke housing.
Verify that the line leading down to the intake manifold's exhaust crossover isn't leaking.
If you have good vacuum at the choke housing port and the line is sound it should heat up very quickly.
If it doesn't heat up quickly (usually too hot to touch it in about 30 seconds or so) then you have one or more problems. Either there is a vacuum leak before the heat tube, in the heat tube or the exhaust crossover passages in the intake are plugged or blocked.
The actual choke dial on the side of the carburetor is fully adjustable for how long it stays on but it will not work correctly unless there is an adequate heat source from the hot-air system.
I'll add here that the hot air system is a "closed system", bringing in filtered air from the rear of the carbs airhorn, pulling it thru the metal tubing in the intake, then supplying heated air to the choke on the side of the carb.
I'd start out by verifying that the choke is set correctly, most are marked with a line on them and there will be a "range" on the choke housing from rich to lean. Rich to lean simply means how long it will stay on after start-up.
We don't see too many factory hot air chokes fail, but we do see a lot of them "crack" and develop vacuum leaks where they seal on the housing which pulls in cold air instead of heated air, so something else to check while you are troubleshooting the problem.......Cliff