What is the code that set the light? There is your first clue.

But it CAN be the CPS, they usually act up at high temperature (that is, after the car is really warmed up) and sometimes the car won't start until it cools 20 minutes or more.

Get the code, and maybe order a BOSCH CPS (don't settle for a generic one, you'll be chasing weird stuff for weeks ...) They are easy to change.

Yea, CPS is the first guess. I carry a spare in my trunk - haven't needed it in 95,000 miles but many do.