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. 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'.

By the way, 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 hot springs of Siberia are located near the city of Tyumen. they are also more published and probably seeing a lot more visitors. 

There is a hot spring located just 5 km's from the city, named Verkhniy Bor 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, nashural 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 can be found on panaramio. 
The hot spring also has it's own website, aptly named vbor.ru.

Tripadvisor refers to this hot spring as Avan (I think) and the Russian reviewers give this hot spring four stars.

Verkhniy Bor, source

Gassy
Further away from Tyumen (27 km) is the hot spring of Sosnoviy Bor (website). Tripadvisor also hands out 4 stars here. 
It can also be referred to as Yalutorovsk.  Virtualtourist once had an extensive entry on the hot spring of what they referred to as Yalutorovsk:

'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 :-)'.

Now why has this link now disappeared?

Finally  some translated information on Tyumen hot springs, making the two hot springs clearer:

'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'.

There is no infrastructure though, so pull up to the pool as close as possible. You’ll have to change clothes in a car and what’s more to run good 30 meters to the water in your bathing suit! That was a challenge with outside temperature -25. What’s more, one of my friends left slippers home and had to run barefoot. Needless to say, he sobered up immediately!

Sosnoviy Bor, source

Watercolours
So I hope I am not confusing everybody. As further west are hot springs near Turinsk by the name of Akvarel. Tripadvisor has also been here and the three reviewers have afforded it just three and a half stars.
Yet again there's a Russian language website through which I learn that the temperature is 35°C, it's 20 km from Turinsk town and renovations took place in 2013. Also this gem of info:

'A little history: In Soviet times, this place was Chekunova Hydropathic-worked doctors took patients. But something went wrong and this looked like a old abandoned building that was restored, rebuilt and opened a new set of watercolors'.

 More info can be had from this English website as well as the following picture:

Photo's from the past show a much more rustic and pleasant looking place. If I am not confused this from nashural concerns the same place?

Southeastwards from Tyumen (100 km) at most probably a town named Zavodoukovsk lies another hot spring, quite rustic. Named Beryozovka, this Russian website has some photo's:

Doesn't look too hot. But apparently hot enough, this hot spring came a a failure of the oil exploration industry. 

Two hundred km's northeast of Tyumen is another possible hot spring, named  Dubrovnaya (?) near the town of Tobolsk (source). It could also be named just Tobolsk ... (source). This is a website with more info.

Elsewhere this Russian website has a list of possible hot springs near Tyumen, unfortunately not all too clear. Probably this is the holy grail for this section. Can someone assist? Because this website mentions 7 hot springs near Tyumen, above are only 5 ...