Kiuas is the heating element of a sauna. At the bare minimum, as in the smoke sauna, it is only a pile of rocks, which are first heated up with a fire, then the fire is put out and the kiuas is used as a heat reservoir. This is time-consuming, but still in use by some enthusiasts; interestingly, its development still continues. Modern combustion technology enables warm-up times of only 2 hours instead of 5 hours.
In the newer technology, as found in every house, a special stove is used, where the rocks are kept in a metal box or cylinder. The stove heats up the fist-sized stones, which act as a reserve for heat. Water is thrown on the hot stones, so that it evaporates. This humidity/heat conductivity change is called löyly. The softness of the löyly depends a lot on the kiuas. The bigger the kiuas, the more there are stones, and so the löyly is softer.
A kiuas can be powered by burning wood or by electric resistors. In a electric sauna, the stones are evenly distributed on the resistors. A clock and a thermostate control the electricity. An electric kiuas usually heats up in 1/2 to 1 hours. A wood-burning kiuas has a combustion chamber under the stones. The has a stove pipe, so that no smoke gets into the sauna. This kind of kiuas takes a lot more work, and heats up slower, in an hour, but it's worth it.
The original kiuas was simply a pile of rocks, and the first industrially produced kiuases were a development of this: they had an immensely large, closed cylinder full of rocks, which was heated with an equally large combustion chamber. Water was thrown in from a hatch in the side of the cylinder. For homes, these are about one to two cubic meters in size. In common saunas, they are two stories high and about three meters in diameter. Such behemoths are still in use in some saunas built in the first decades of the 1900's. After they've been heated up, they require no heating, since the amount of stored heat is enormous. A new concept was continuous heating, with only a bucketful of rocks for a reservoir. They warm up quickly, but require constantly adding more wood to the fire. This problem is solved in electric kiuases.
It had been a mystery for a long time why the wood-burning kiuas is so much more liked than the more user-friendly and handy electric one. The reason for this is that the flame and the evaporating water produce negative ions. These ions are beneficial, unlike positive ions, which are released by bare resistors. When the positive ions outnumber the negative ions, people get headache and miscellaneous symptoms, while negative ions may actually be beneficial.
An electric kiuas is a really big resistor, so you wonder how much does it use electricity? Its power is 3-9 kW, so it takes 6-27 kWh per one 2- to 3-hour heating. In Finland, this costs about 0.30-1.35 euro. An electric kiuas might also cost more, because its stones have to be changed from time to time. An electric device doesn't last as long as a simple fireplace. The stones have to be changed periodically or the kiuas will break up. The heat expansion erodes the stones quickly, and they push between the resistors, bending them.
A special stone called löylynhenki can be placed in the kiuas. In the summer cottages, which are far away from everywhere, hot water can be produced with a kiuas. Around the cylinder that holds the stones, there is an annular tank, which you fill with water from your favorite unwarmed water source.
The price of all this fun: a normal kiuas (3-9 kW) costs 85-340 euro, no matter if it's electric or wood-burning. For 20 euro, you can get a box of ceramic stones that look like pieces of wood, but simple dark green olivine stones cost only 13 euro. (This price was in K-Rauta in Vaasa.)
The word kiuas has the etymological root *kiuka "pile of stones", and the synchronic root for attaching case endings (other than the partitive) is kiukaa-. That is to say, kiukaalle "onto the kiuas" and so on, but partitive kiuasta "some/at/of the kiaus". The nominative form kiuas is not the "plain" form, which is nothing unusual in Finnish. The telic plural is kiukaat, and the atelic plural is kiukaita.
Sources:
The Sauna Site. Kiuas. http://www.saunasite.com/
Adato Energia Oy. Sähkökiukaat - Sähkönkulutus. http://www.energia.fi/koti/kiukaat/