Polybenzimidazole-based electrochemical hydrogen pumps (EHPs) allow hydrogen separation from gas mixtures at low cell overpotential. An operating temperature of up to 180 °C provides robustness towards catalyst poisoning by common impurities in steam reformate, like CO or sulfur compounds. Electrochemical impedance spectroscopy (EIS) coupled with the distribution of relaxation times (DRT) analysis is performed on single-cell EHPs supplied by H$_2$ contaminated with N$_2$, CO$_2$, and CO to investigate and quantify the underlying physicochemical processes. By systematically varying the operating parameters, five different processes were identified in the DRT spectrum: the proton transport in the electrode, the hydrogen evolution reaction (HER), the hydrogen oxidation reaction (HOR), the mass transport (MT) in the anode gas diffusion electrode, and the movement of phosphoric acid anions from the cathode to the anode at high current densities. At high contaminant concentrations, the HOR and the MT resistances increase. The HOR inhibition is dominant for CO, while for N$_2$ and CO$_2$, the MT resistance increase is more pronounced. At 180 °C cell temperature, the performance with 50% CO$_2$ in the gas feed was worse than with 1% CO, highlighting the possibility of operating an EHP with a CO-contaminated gas feed at elevated operating temperature.