Does soaking in natural hot springs have any health benefits when compared to soaking in heated non-spring water?

Question

There exists a common belief that soaking in natural hot springs has significant health benefits. For example, Hotelexecutive.com claims that:

So What Exactly Can Soaking in Natural Hot Springs Do?

1) Improve Circulation - Bicarbonate hot springs are thought to help with blood circulation, hypertension, nervous imbalances and atherosclerosis.

2) Treat Skin Infections - According to the website Alternative Doctor, bathing in sulfur-rich hot springs helps treat dry scalp and arthritic pain as well as internal problems such as menopausal symptoms and digestive disorders.

4) Detoxify - It is believed that bathing repeatedly in hot springs can help tone your autonomic nervous system and normalize your endocrine system, as well as release toxins in your body through sweating.

5) Boost Immune System - Some proponents believe that iron content in hot springs, along with other trace minerals, might help build your body's immune system, making it stronger and more able to fight infections.

This leads to two questions:

1. Is there any scientific proof that soaking in hot spring water leads to the above mentioned health benefits?
2. Assuming so, can the same effect be achieved by soaking in heated water from a non-spring source, such as a lake or an ocean?

Answer 1

Today I learned that medical geology is a thing.

This journal article gives a nice survey of "geologic benefits", including a section on hot springs:

Visiting hot springs and thermal baths for prevention and cure of a variety of illnesses, once popular in the USA, has fallen out of favor.... The study of the therapeutic benefits of naturally occurring mineral waters is known as balneology. In the United States, this science is not well known, and is seldom practiced. However, throughout Europe and Japan, balneology and hot springs therapy is very much a part of routine medical care....

There appears to be little in the way of epidemiological support for such claims in the U.S. medical literature. A brief review of the National Library of Medicine abstracts of articles dealing with the therapeutic effects of hot springs revealed that most authors are from Japan. Other authors were from Germany, Turkey, China, Portugal, Greece, and Israel. The one article by a U.S. author reported on the historic use of hot springs to effectively treat venereal disease.

Ultimately, the evidence on balneotherapy is no more effective than placebo. Certainly soaking in hot water is somewhat helpful for arthritis, and it's easy to say "well, what's the harm?" Certainly there are downsides, such as brain-eating amoeba.