All easy things to check. Another common issue (still with the choke) is that the fast-idle cam simply gets stuck in a higher position. Once the heat releases the mechanism's tension, the cam comes down by gravity only (at least on some carbs) and if it's a little sticky might not release fully.
My first go-to thing is a nice cleaning with carb cleaner, then a quick lube with something light like WD40. It's not a permanent cure, and you don't necessarily want to use a real sticky lube like LPS or something that's going to eventually gum up the works. But it's a good quick test to see if anything is sticking.
If that doesn't work, then you can dig into the mechanical aspects and adjustments.
How high does it idle right off the bat?
Have you removed the air cleaner housing to see what's going on at the carb? If so, how long before you can see the choke open up?
You should be able to watch it open over the first few minutes, and see the fast-idle linkages do their thing.
Paul