This questions of calorie burn for Bikram comes up now and again. The extremely high reported calorie burn is often found on Bikram related sites, but not supported by others, and I have never seen any research that supports it; except, perhaps people doing it who say they used their heart rate monitor and they burn way more calories. The problem with this is that the heart rate is increased to deal with cooling the body, not due to the physical exercise.
Heart Rate calculations for calorie burn need to meet the expectations of the underlying math, and these are typically related to the heart rate increase being based on cardio activites such as running and biking. As we move away from these types of activities the reliability of the estimates goes down.
My clearest example is that of Riding a rollercoaster. This will raise the heart rate, but it does not burn any more calories than any other sitting.
Good running and be Careful out there
Certified Chi Running and Chi Walking Instructor
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