A wire electrode discharge machining apparatus includes a hollowed beam member 16 coupled with the front side of a column 4 by a guide vertically movable with respect to a table 2, a pipe 17 for supplying to the beam member 16 a machining liquid 15 whose temperature has been controlled by a machining liquid cooling means 13, a pipe 18 for supplying to a machining bath 10 the machining liquid 15 that is supplied from the pipe 17 to the beam member 16, a covering member 19, made of adiabatic material, for covering the outer surface of a temperature sensor 14, which is attached to the body proper of the wire electrode discharge machining apparatus, a cover 20 for covering the apparatus body, an adiabatic member 21 attached to the cover 20; and a fan 22 provided inside a covering structure including the members 20 and 21.