Middle English (in the sense 'sweating room'): from Middle Dutch or Middle Low German stove; perhaps related to the noun stew¹. Current verb senses date from the early 17th century.

• stew from Middle English:

  When stew entered the language it referred to a cauldron or large cooking pot, not to what was being cooked in it. The source was Old French estuve, probably based on Greek tuphos ‘smoke or steam’, which is also where the fevers typhus (late 18th century) and typhoid (early 19th century) come from, because they create the kind of stupor that is associated with smoke inhalation. The verb ‘to stew’ originally referred to bathing in a hot bath or steam bath. It was not long before the idea of heating people in a bath had changed to heating food in an oven, specifically cooking a dish of meat and vegetables by simmering it slowly in a closed vessel. Stifle (Late Middle English) probably comes from the same Old French root, and stove (Middle English), originally a ‘sweating room’ in a steam bath, may be related. See also seethe