When it happens ... are the keys in your pocket with any chance of hitting anything that may cause the "condition" you mention? sometimes, SIRI will talk to me when my iPhone is in my pocket and the button gets activated somehow. Normally, remote start will only happen if you press the lock button on the key FOB, followed quickly by the remote start button. My Cruze wasn't an automatic though, so I didn't have remote start. If it's got push button start/stop, is there any chance that button could be stuck? Had a stuck door lock/unlock button on my Volt, but never would have guessed that's what was keeping my car doors from locking automatically when I got out, because the button looked like it was fine. Just some points to ponder.
I have an aftermarket remote start, and if i hit my lock buttom twice on the stock key fab it does that. Sometimes it starts when my keys are in my pocket, sometimes it just turns over and shuts off. If you do not have an after market one, was the car used? Maybe the person before got one and did not turn in the remote with the car.
We're sorry to hear you're having difficulty with your Cruze. If you're thinking you'd like to have a certified Chevrolet dealership take a look, please feel free to contact us by private message. Be sure to include your VIN, mileage, contact information, and preferred dealership.