Likely an o2 sensor issue. I had as similar issue with my car minus the check engine light being on.
O2 sensor is not working right or is screwing up signal to the ECU. It's detecting a lean A/F ratio, which is not good for the motor. Basically it thinks it's getting too much air and not enough fuel.
When the car is cold, it runs open-loop, meaning that the A/F ratio is based off the ECU alone -- no o2 sensor feedback. Once the car warms up, it switches to closed-loop and starts adjusting A/F ratio based on the input from the o2 sensors.
A bad sensor could surely describe the issue you're seeing. I cannot remember which o2 sensor was the issue for me though. But you might want to look into them.