Context. Measurements of the Sunyaev-Zel'dovich (hereafter SZ) effect distortion of the cosmic microwave background provide us with an independent method to derive the gas temperature of galaxy clusters. In merging galaxy clusters the gas distribution is inhomogeneous and, therefore, the method of temperature measuring based on the SZ effect should be more relevant than that based on an X-ray emission analysis. Aims. We study a method for measuring the gas temperature in merging clusters by means of the SZ effect. Methods. Our calculations of intensity maps of the SZ effect include relativistic corrections considered within the framework of the Wright formalism and utilize a cosmological numerical simulation of a merging galaxy cluster evolved with its baryon physics. Results. We found that the gas temperature in merging clusters can be inferred from the ratio of the SZ intensity at a low frequency (128 GHz) to that at a high frequency (369 GHz). This SZ intensity ratio permits us to reveal prominent features of the temperature structure caused by violent merger shock waves. Therefore, measurements of the ratio of the SZ intensities are a promising tool for measuring the gas temperature in merging galaxy clusters.