I'm guessing you have the 3.5 engine. Sounds like a heat issue with one or all of the sensors. Once it's cool enough is starts okay. Yes they do need replacing as your computer is compensating with default settings if it can't read the sensors. Crankshaft Position sensor is the number one thing that always goes bad on all Intrigues. I have replaced mine twice in 100k. Both were Delco parts. I bought the cheapy one last time as it doesn't seem to matter whether you buy Delco or not. GM quality I guess. That sensor is under your starter. Get it from
http://www.rockauto.com/catalog/x,ca...,parttype,7196 . Like I said I bought the cheapy and it works fine. I checked all your codes and they all indicate Crankshaft sensor.
If you have a ratchet set you could replace it in about an hour having never done it before. Once you take off the starter take off the plastic cover to the fly wheel. This will make it much easier to reinstall as it takes some wrangling to get the starter back in just right. One bolt holds on the Cranshaft sensor. Disconnect the battery first!
Good luck!