Why would you need a check valve?
Somebody once told me that such a system could even work without a pump due to the cooler water being heavier. This person was not an authority, but he seemed enthused.
But what I am wondering is why you think a reverse flow would happen, and what the penalty would be if a reverse flow did happen? I would think that your pump would be a very low pressure pump. Wouldn't you be concerned about the back-pressure that you would be introducing?
I am not a pro, and I am not speaking from experience.