Expanding

Siberia is definitely a wide expanse of openness, and what with the many hot springs situated in the area around the Baikal lake, one would expect a couple of hundred hot springs to be located in Siberia. At least.
Wrong. After much research there only seem to be a few. Or at least there is so little info available on internet. Or there may be hot springs still waiting to be discovered.

Cold Fame

Superlatives assume Siberia to be very cold. And apparently no place on earth gets colder than Oymyakon (Wikipedia). Located 3 days drive from Yakutsk,

'Oymyakon boasts an average winter temperature of -45C, with a one-time world record low of -71.2C
...
Ironically, Oymyakon means “non-freezing water”, situated as it is to a nearby hot spring'. source

Even though this is ironic and might lead one to think that there can be no better way of illustrating the contrast by looking into more 'depth', alas the cold wins from the heat, at least in reporting on internet. Even such absurd news such as

'Nippy cows wear bras in Russia'

get a blog entry.

Possibly dinets.travel.ru refers to Oymyakon (Oimyakon) when focusing on orchids but mentions:

'Some rare and beautiful flowers, normally found only in Southern and Western Siberia, can be seen around hot springs in the uninhabited area between Suntar-Hayata and Verhoyansky Range. In this mountain chain, 3 times as long as Sierra Nevada, there are only two small villages and three mines. Hot springs do not freeze in winter, and I discovered a wintering population of brown dippers (Cinclus pallasi), diving in the water despite the frost'.

Possibly referring to the same, is the mention of Tjoply Kljuch (Tyoply Kljuch), which this Italian blogger refers to as having a 'fonte tiepida' (warm source). LP Thorn Tree also mentions:

'There's a small village called Tjoply Kljuch where there's a hot spring'.

Btw. Tyoply Kljuch is yet again mentioned by Wikipedia as a 'warm spring' on the Sea of Japan coast, north of Vladivostok, south of the Amur, somewhere totally different.

Complicating things even more is this blog entry mentioning that the near by Oymyakon, Tomtor, has a hot spring by wideview.it:

'A stream that never freezes, because of hot springs. The vapour, coming out continuously, freezes instantly over the trees all around, creating very bizzarre shapes'.

Funny

The most western most hot springs of Siberia are located near the city of Tyumen. More published and probably seeing a lot more visitors. There is a hot spring located just 5 km's from the city and it

'... is well developed to accept tourists. Accommodation, meals are readily available. The water is highly mineralized having temperature of 45 degrees Celsius and cures many unhealthy conditions'. source

There are a few soak experiences on internet such as the blogs by englishrussia.com and this from Sergey Gershtein:

'There are hot natural springs that are said to be funny to visit in winter. It was funny indeed'.

He unfortunately fails to expand why they are funny. More photo's on panaramio.

The source above, roadtripsacrossrussia.com, describes there being another less developed hot spring 30 km from Tyumen, most probably a reference to Yalutorovsk (or Zavodoukovsk). Yalutorovsk is 70 km from Tyumen (wikipedia).
An entry on virtualtourist describes Yalutorovsk as follows:

'In some dozen kilometers from Yalutorovsk there is a hot spring. It is just in the forest, so the correct destination I can't say. In any way if you ask residents, they will tell you I suppose. It was funny to sit in the hot water when the snow was everywhere around. If you're in the center of the spring you may light it up because there is gas. It is not dangerous :-)'.

'it is fired'.

by bugulma

Other translated information reads:

'A comfortable hot spring is located 11 kilometers from Tyumen - in the Upper Forest. There is a marble pool in the open air is filled year-round warm water. Pool length of 20 meters, a width of 6 meters and a depth of 1.5 meters is divided into two tracks, the temperature of water in them is different. It is surrounded by pines and ornamental palms, near the falls beautiful artificial waterfall.
Near the hot spring are changing rooms and showers. This source is considered to be landscaped, as located near hotels, lodges and cabins for tourists, as well as all the amenities - gazebos, barbecues, and equipped with slides, ski and skate, skating rink, as well as a cafe, billiards, sauna, solarium, Karaoke and much more.
Wild hot spring is located 30 kilometers from Tyumen. There are no facilities - it is possible to live in tents or go to the city'.

Help

Moving eastwards, Krasnodar region has a few hot springs with not so much more info other than this:

'Mineral springs are of great interest and form the basis of health resorts in Goryachy Klyuch [the name means "hot spring"], Khadyzhensk, and Maikop and the Krasnodar Hydropathic Center. The mineral waters of Goryachy Klyuch and Maikop have a well-deserved reputation as table waters. The territory's hotel business is expanding. A favorable climate, warm seas, mineral and mud springs, and scenic mountain and coastal landscapes have combined to make Krasnodar Territory one of the most important tourist regions of Russia and the CIS'. source

On Goryachy Klyuch Wikipedia adds little, but the above is about all the info available on Krasnodars hot spring resorts.

So where does this leave us?

With most of the Asian continent close or north of the Himal already featured, it seems the only place left is Russia's eastern frontier, Kamchatka. So look forward to an expansive entry on this including the Kuril islands.