It is these type of experiments which should give you your answer on calorie expenditure. Core body temperature during menopausal hot flushes. What is chemically getting flushed out of the body in a hot flash that is different from regular heat regulation perspiration as it has a characteristic odor unlike regular perspiration and is not as salty. I have seen no information on that in the literature. However, I have seen a study on a substance which lowers LH when inhaled.
Visceral fat tends to be related to insulin levels.
The more insulin, the more abdominal fat. So the fat deposition pattern is hormone related. I'd guess it is simply a matter of feeling more heat because there is more fat for insulation. Modulation by sex hormones of the membranous transducing system regulating fatty acid mobilization in adipose tissue. Prostaglandins Leukot Essent Fatty Acids.