We present the results of numerical and experimental study of the photoconductive antennas (PCAs) based on GaAs and its ternary compounds. We produced three photoconductive materials with different indium content, which then were applied for fabrication of the THz PCAs. These PCAs were used as emitters of the THz pulsed spectrometer. We evaluated the stationary transient current generated by the PCAs, simulated their I-V characteristics, and compared them with the experimental ones. Using the finite integration method, we studied the thermal properties of the PCAs and demonstrated significant influence of the heat-sink on the leakage currents of the InGaAs-based PCA. We showed that the heat-sink reduces the operation temperature of the InGaAs-based PCAs by 40-64 % depending on the indium content. The observed results might be interesting for applications of the PCAs in THz pulsed spectroscopy and imaging.