The thermoelectric coupling characteristics of a kind of n-type piezoelectric semiconductor nanowire (ZnO) were studied with finite element method. The effects of external temperature on internal distribution of mechanical, electric and current fields of the ZnO nanowire were analyzed. And effects of the linearization of the constitutive equation on electric parameters were discussed. The results show that the external temperature greatly affects the electric field, carrier concentration and electric current density. The electric field, carrier concentration and current density derived from linear and nonlinear constitutive relation differ greatly, the maximum difference are 24%, 32% and 68%, respectively. A large error will appear when one adopts linear constitutive relation to analyze electric properties in piezoelectric semiconductors.