While sitting in a sauna, you burn only the calories that your body regularly uses. According to WebMD.com, sitting in a sauna or steam room will cause you to sweat out any excess water your body has retained, but it will neither cause fat burn nor burn extra calories.
According to WebMD, the human body burns a certain amount of calories every day simply to maintain basic functions like breathing and organ function. If you sat in bed all day, your body would still burn this amount of calories, although the specific number varies based on your height, weight and gender. Any exercise or activity you do beyond this burns extra calories on top of that amount. Sitting in a sauna or steam room is just sitting, so it doesn't elevate the heart rate enough to burn extra calories. Steam rooms and saunas may cause you to sweat out water weight, which is just extra water retained by the body, but they will not cause fat loss by burning calorie.