Looking for some wisdom.  Recently purchased a stock 2007 S40 with 4500 miles.  Was concerned bike would not idle for prolonged period even in 40F weather.  Appears to be cured now, but want to understand why.  Sequence of events follows.

Engine would not idle for more than 15 to 20 minutes.  During this time, had to keep increasing throttle with idle adj screw until it was all the way in.  Revving motor suggested plug was not getting fouled.  After engine stalled or I shut it down, it appeared to turn over just fine.

Found vacuum fuel valve was not closing when engine off and possibly that flow through valve was being restricted regardless of valve setting.

Found rubber seat for the vacuum valve was badly misshaped.  I pulled out the seat and made sure fuel appeared to flow freely after it was installed.  

Have resorted to pinching the fuel line to shut off fuel until I replace with the manual valve.

Engine would not start after changes to fuel valve.

Removed the plug.  It was wet with fuel.  Found engine has been running rich.  (Was expecting it to show lean running.)  Drained the gas from the carb and cranked the engine for a bit with plug removed.  

Put cleaned and gapped plug back in.  Engine started immediately.

Tried to let engine idle again but still wanted more and more gas to idle.  

Began to worry that there was gas in the oil.

Drained oil and found it had a strong gasoline odor.  Yikes!

Put in fresh oil and filter, ran the engine, drained the oil again, and put in more fresh oil.   Engine seemed to be running smoother but it was subtle if at all.

Tried letting engine idle again.  Found idle screw wanted to be adjusted further out when cold, less throttle, compared to before.  Engine idled for 30 minutes with no need to touch the idle screw.  Life is good.

Why wouldn’t the engine idle before?

Why would you want to idle your motor for 30 min? Asking for it to over heat.

The Savage engine does not have much oil flow at idle, and if your idle is too low......the pump does not flow enough oil to send oil up to the top end.  This forum has experienced several ruined top ends (cam bearings) from engines run with too low of idle speed.

You really should not run (or idle) an engine for more than a few minutes without riding it and gettting some cooling air flow to the engine.

I'd love to know how they test cooling on these engines. I've never seen anything from the factory about heating while stopped or idle times.

I am of the opinion that a good air cooled engine should be able to idle indefinitely without overheating.  If it has forced air cooling it should run at any speed without overheating.

You are stating that you adj the idle adj screw all the way in.... left side carb knob with spring?

Did you try to adj. you air/fuel mix screw? ...right side carb standard screw..has a cap over it.

Definitely replace your vacuum petc0ck with a manual one, it will keep the gas in your crankcase from happening again in your future (well, if you turn it off everytime..minor inconvenience).