>>> The heated room obviously makes you sweat heavily, which helps to flush away toxins and impurities and improve circulation.
Yoga has done wonders for my running and doing Yoga in a heated room probably has some good benefits, but the "sweating out toxins" thing is a myth. From Columbia University's Health Services:
http://goaskalice.com/7781.html
". . . inducing heavy sweating is not an effective method of ridding your body of toxins — though it's very good at ridding your body of vital fluids, potentially leading to dehydration. Sweating releases traces of toxins (less than 1% of the body's total content), but in reality, its sole purpose is to prevent overheating. The liver and kidneys (not the sweat glands) are the body's true detoxifiers. They filter toxins out of the blood and the body releases them through urine and feces."
A good a good electrolytic solution is 1 cup water, 2 tablespoons freshly squeezed orange juice, 1/3 teaspoon of salt (preferably celtic sea salt).
>>> 5000 years old, yoga
While the philosophy and practice of Yoga is likely thousands of years old, the Asanas (Postures) aspect of Yoga in it's current form is only about 100 years old.