In case anyone else was wondering how the auto keep-warm feature is implemented: it's a CloudWatch Event that runs the Lambda every four minutes by default.
While this probably keeps the majority of the requests warm, I would expect that there would still be some cold ones every now and then. Amazon doesn't provide a guarantee in how the containers get recycled.
We did some analysis[1] on cold starts in AWS Lambda, and found that there is a cold start if there's no activity for 5 minutes, or regardless of activity, there will be a cold start every 4 hours from creation of the underlying VM.