This product was advertised in the 1970s - 1981, when the couple behind it, Jack and Eileen Feather, was indicted on mail fraud and false advertising charges. They also sold several other sham products, including a bust enhancement device. They eventually paid $1.1M for materially false claims and stopped selling their products.

In 1971 the USPS commissioned a test of the Sauna Belt by a physician in 20 subjects, which concluded:

the variations in girth of less than one-eighth of an inch that occurred were due to normal variations which might occur without regard to the following of Respondent's plan; that there were more increases than decreases in girth during the study as a whole; and that the following of Respondent's plan produces no significant results in terms of the girth of the user.

You might change your hydration status by sweating, but that weight returns when you re-hydrate. The instructions advised a lower calorie diet and exercise, which can yield weight loss, but you don't need the company's belt or pants to do that.

Monty Python had a spoof of these pants.

There is still a market for similar products today.