Thermoelectric devices (TEs) can achieve direct conversion of heat and electricity by semiconductor materials, coupling of heat transfer and electric conduction is important to accurately predict the performance of TEs. This paper develops a general, three-dimensional numerical model of TEs with consideration of coupling of temperature field and electric potential field. The model is used to figure out the performance of thermoelectric coolers (TECs) with the temperature-dependent thermal conductivity, electric conductivity, and Seebeck coefficient of semiconductor materials. A miniature TEC is considered and Bi₂(Te_0.94Se_0.06)₃ and (Bi_0.25Sb_0.75)Te₃ are selected as the n-type and p-type thermoelectric materials, respectively. The effect of parameters such as the temperature difference and the current is investigated under conditions of variable material properties as well as radiation and convection heat transfer occurred between the TEC and the ambient gas. The results show that the variable properties and the heat losses to the ambient gas have significant effects on the cooling capacity and the coefficient of performance (COP) of the TEC. Three-dimensional temperature distributions within the semiconductors is observed under convective boundary condition and it becomes remarkable at large temperature differences and high currents.