Abstract: A theory of an electron-heating mixer which makes it possible to calculate all the characteristics of the device is developed. It is shown that positive conversion gain is possible for such a mixer in the millimeter to near-infrared wavelength range. The dynamic range and the optimum heterodyne power can be selected from a very wide interval by varying the mixing element volume. Measurements made for Nb within the frequency range of 120-750 GHz confirm the theory. The conversion loss obtained at T=1.6 K and normalized to the element reaches 0.3 dB in the intermediate frequency band of 40 MHz; the possible noise temperature is 50 K. The estimation of noise temperature and output band for YBaCuO at T=77 yields 200 K and more than 10 GHz, respectively.