The optimal performance of a thermoelectric device used as a refrigerator is discussed by using the rate of refrigeration and the coefficient of performance of the refrigerator under the influence of three main irreversibilities which are heat conduction, heat leak, and Joule heat. The coefficient of performance and the operating current of the refrigerator at the maximum rate of refrigeration and the operating current of the refrigerator at the maximum coefficient of performance. The reasonable ranges of the coefficient of performance, the rate of refrigeration, and the operating current for the refrigerator are determined. The results obtained here have more instructive meaning than those of non‐equilibrium thermodynamics for the optimal design and operation of practical thermoelectric refrigerators.