2003 Hard starting / fuel purge ?

My 2003 Accent takes 2 cranks to start... the problem occurs more when it is hot outside (phoenix in the summer).  Also once the enigine is running it makes like a dieseling noise when you let off the gas like a timing issue, but then clears up once the enigne warms up.  So the symptoms are the engine is rough when its cold, but only when its hot outside.  Any ideas?
 
Also, I've recently noticed a noise coming from the underneath in the rear by the gas fill just after the engine is shut off.  Its sounds like an electric motor for about a minute then like a valve shutting or opening?  I've reviewed some books and think its something like the fuel purge canister and valve?  Should it be making that noise after shutting down the engine?
 
Any thoughts would be much appreciated.. thanks
Go Hyundai!  Wish I had a tiburon :)

Hard starting due to low fuel pressure perhaps.

A.