We report on measurements of the microwave-modulated Shubnikov-de Haas (SdH)-like oscillations in a GaN/AlGaN heterostructure. This technique greatly enhances the visibility of the SdH-like oscillations while keeping the carrier density constant. The enhanced SdH pattern is attributed to the hot electron effect. We find that the amplitudes of the SdH-like oscillations increase with increasing microwave power. In our case, the logarithm of the SdH-like amplitudes is proportional to the inverse of the applied perpendicular magnetic field, with striking similarity to a conventional Dingle plot. Moreover, the slopes of the Dingle-like plots are approximately constant at different applied microwave powers. However, in our case, during the microwave pulse the electrons possess an equivalent temperature higher than the lattice temperature. After the end of the microwave pulse the electrons relax to the lattice temperature. Therefore the electron temperature is not constant over the whole measurement range. Thus our new experimental results point to a deficiency in the existing theory and the urgent need for further theoretical studies on electron transport in the presence of microwave modulation.