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Wood is rarely used as a fuel.

Gas, oil, electricity, district heating or geothermal heat are used. Prices will be roughly similar, where the supply exists.

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Wikipedia says "The wood stove sauna is the most common type of sauna [in Finland] outside of the city areas".

In the context of "It's amazing if Finland has solved poverty to the level that every household can afford to set aside the space for a sauna and costs of running it.", and rural areas tend to be poorer than city areas, discussing wood as fuel for said saunas seems relevant.