The authors used the photoelectron method to study plasma X-ray spectra and to determine the electron temperature of the plasma, Te. The measurements were made on the T-13 tokamak and the OGRA-4 mirror trap using a five-channel photoelectron spectrometer in the 50 eV to 40 keV energy range with a time resolution of 1 to 20 ms. The results are in good agreement with data obtained by Thomson scattering and by the filter method, and also with calculations of Te based on plasma conductivity. It is shown that at large modern facilities a photoelectron spectrometer with no load limit can record 104 to 105 times more photons in a given time interval than an X-ray pulse height analysis system. Moreover, the photoelectron spectrometer has low sensitivity to hard X-rays and neutron radiation and can therefore be used at facilities with reactor parameters in experiments with D-D and D-T plasma.