Are there any trouble codes? Some of the national brand auto stores will check codes for free. When was the last tune-up? How is the fuel pressure?
There was a bulletin about a possible egr problem, may cause any or all of these problems, hard start after hot soak--rough idle--start & stall with cold engine. You would need to trouble shoot the egr valve, mainly by blocking it off.
As far as temp related, the cts might cause some issues.