How many calories does swimming burn compared to other cardio?

The calorie counters on the machines I’ve used tell me that rowing burns the most calories, then the stair climber, then the treadmill, then the eliptical, and then the stationary bike (if those calorie counters are accurate). How many calories do I burn swimming compared to those other activities? A coach I know told me that swimming doesn’t burn very many calories because the cool water prevents the body from heating up the way it does with other activities, is he right?