"as if he had just come out of a Russian bath"
Russian baths, or banyas,
are an important part of Russian culture. They are a form of sweat bathing similar to saunas. Bathers sit in incredibly hot steam rooms, washing and beating themselves with birch twigs to improve their circulation. Afterwards they cool down by standing outside, or by immersion in cold water; in winter people roll in snow. Traditionally, aristocratic households would have their own steam room whereas villages would have a communal bathhouse.