Sounds like a bad connection to your engine temp sensor. It tells your computer the temp or your engine so it can direct the fuel system to change the fuel mix etc. correctly for the engine temp. It will work when cold because it defaults to cold temp operation, but once the engine starts to heat up, the output should change. If it doesn't, the engine will slowly begin to run more rough and in many cases stall. Once cold, will start up with no problem. Sometimes the connection gets oxidized due to temp and moisture changes. Try pulling it off and re-seating it. Can be found under the black plastic vented cover that snaps onto the big black air filter housing in the engine compartment. Pull it up to remove. Under it, you will see a few sensors that look like spark pugs. The one to the left with one wire connects to your temp guage on your instrument cluster. The one to the right with the larger connection is the one you want. Pull the connector off (with care as they get brittle) and put back on. Do this a couple of time to clean the connection. Could also be bad, which requires replacement. I think about $50 for part, use a spark plug socket and use thread lube to ensure easy removal in the future. Keep in mind, you car has been sitting so you could be dealing with other stuff. I would change oil, plus, air filters anyway. Hope this helps