If I know a saw is prone to vapor lock or start lean when hot, I may choose to choke it off, even going as far as revving it up all the way before choking it off to prime the engine full of gas (I do this with a certain ms180 in the summer). Then, while it is working through the flooded condition I left it in, it is able to work through the vapor lock or whatever is causing the lean condition. You have to be careful doing stuff like that, because it can make starting really hard if you get it wrong.
I remember experimenting with different shutdown techniques with my 572 while milling in 35-65 degree weather, because sometimes it was hard to restart. Not really that hard, but 5 or so pulls when warm, trying different things with the choke, rather than just 1 pull. If I remember correctly, I'd choke it off at idle, then for restarting I set the fast idle, but with the choke off. For the most part it worked for my particular case. It's good practice to let the saw idle for a while, like 30 seconds or so, before shutting it off to let the engine cool while fuel is still flowing, so it doesn't heat soak the carb causing vapor lock. Heat soak in an autotune could cause the temp sensor in the carb (I think there is one) to get a false reading messing up the fuel mixture. Too much heat in that case should cause autotune to reduce fuel flow, meaning you may need to choke it when starting, but I could be wrong. I find it helps to let it fast idle for 5-10 seconds after starting, so it doesn't try to die right after starting.
The problem with an autotune feature is that when you try to learn to compensate for its shortcomings, autotune is also changing based on weather and running conditions, so it takes much longer to learn the quirks. That's why I like to have a fully adjustable choke, that doesn't release when the throttle is touched, so I can control the amount of fuel when starting.
It's also a good idea to keep an extra starter pulley or 2 on hand for the 572. They are not built as tough as they should be, and eventually break.