car runs fine when car is turned off problem starts

Are there ever any service engine soon lights coming on? If so, then I would check out any codes, in addition, I would inspect the crank shaft sensor and the ignition module, both of which can cause these types of symptoms. This sounds like a heat related issue, in that once the car is warmed up, something, often an electronic device, is heating up and then malfunctioning. This is a pretty common scenario.