Magnification errors arising from wafer processing cause significant overlay errors in lithography. We have devised a new, simple method that involves changing the wafer temperature to correct magnification errors on an x-ray stepper. A wafer is first heated in the wafer orientation unit, and then it is allowed to cool as it is transferred to the wafer stage due to the temperature difference between the wafer and the air in the chamber. For a given cooling time, the reproducibility of the wafer temperature is less than 0.3 degrees C; and the maximum available temperature change is 1.5 degrees C. The key point is that the placement of patterns on a wafer immediately after the chucking remains fixed regardless of further changes in the wafer temperature, provided that the force holding the wafer to the stage is strong enough. The maximum magnification error that can be corrected by this method is about 4 ppm. This is determined by the maximum available temperature change (1.5 degrees C) and the coefficient of linear expansion for Si. The results of overlay tests revealed the correction controllability to be below 0.2 ppm. When this correction method was used, the total overlay accuracy was found to be 38 nm (3 sigma), which includes mask placement error, etching process error, and so on.