I would first check the fuel line and filter inside the tank, the spark plug, and air filter. The rush of air IMO is normal cause I notice it on my saws. If the filters and plug looks OK after cleaning, then I would suspect a gummed up carb. The fuel line may have a small crack from Corn gas which causes most fuel line to rot quicker IMO.

After checking the obvious first, I would then try try to spary carb cleaner down the venturi and in all the little passages. You can take the high and low jets out, but, you must mark and count the revoluations of the each jet so you can get them exactly back to the same turns, if you don't know how to adjust a carb. or you don't know which way to richen or lean out the carb. You can spary the carb venturi (air intake) while you have the saw at a high RPM. a few seconds won't hurt the saw with no load on it and heat hasn't built up enough to score any parts.

Third, the carb. just maybe out of adjustment. I would try the low screw a 1/8 turn out (CCW) to richen up the idle curcuit. But, I usually clear the carb. first, this way I know I am not creating another problem by adjusting a dirty carb.

You can also check the spark when the saw is hot to see how strong the coil firing, but usually it's an gumming problem, adjustment problem, clogging/sucking air problem form cracked fuel lines or loose carb. mount screws. that's about all the guesses I have. Odds are it's just gummed up. If your not that familar with carb. cleaner or afraid to use it read the instructions on the can and observe all safety precautions.