The new thermal rate equations were built up by taking the linear and non-linear components in the temperature dependences of the Seebeck coefficient alpha the electrical resistivity rho and thermal conductivity kappa of a thermoelectric (TE) material into the thermal rate equations on the assumption that their temperature dependences are expressed by a quadratic function of temperature T. The energy conversion efficiency eta for a single TE element was formulated using the new thermal rate ones proposed here. By applying it to the high-performance half-Heusler compound, the non-linear component in the temperature dependence of alpha among those of the TE properties has the greatest effect on eta, so that eta/eta(0) was increased by 11% under the condition of T = 510 K and Delta T = 440 K, where eta(0) is a well-known conventional energy conversion efficiency. It was thus found that the temperature dependences of TE properties have a significant influence on eta. When one evaluates the accurate achievement rate of eta(exp) obtained experimentally for a TE generator, therefore, eta(exp) should be compared with eta(the) estimated from the theoretical expression proposed here, not with eta(0), particularly when there is a strong non-linearity in the temperature dependence of TE properties. (C) 2009 Elsevier Ltd. All rights reserved.