An anesthetic evaporator unit (2) with an anesthetic container (4) for receiving liquid anesthetic, with a gas line (6) with an open-pore, porous line wall (8) for guiding gas and for enriching the gas with anesthetic, and with an anesthetic-guiding wick (10), which extends from an interior space (12) of the anesthetic container (4) to the line wall (8) in order to supply the line wall (8) with anesthetic from the anesthetic container (4). The anesthetic evaporator unit (2) has a heater (14) for heating the gas line (6). A method for controlling the anesthetic evaporator unit (2) is also provided.