© 2014 Taylor & Francis.In this study, the detailed harmonic analysis of GaN high electron mobility transistor (HEMT) at different temperatures and frequencies is presented. Volterra power series and multi-dimensional Laplace transform are used as a method. The Volterra power series is also solved up to third degree, and the small signal transfer functions of kernels (H1, H2 and H3) are obtained. The relationship between drain inductance (Ld), gate-source voltage (Vgs), impedance (ZL) and the effect of frequency (Fr) to the output gain is identified. Besides, the nonlinear gains of H1, H2 and H3 kernels of the GaN-HEMT are obtained. The inverse relationship between the output gains of H1, H2 and H3 kernels are derived. An unsuitable situation has also been identified for sub-carrier inter-modulation systems. In addition, an asymmetric structure is also obtained between the output gain of H2 and side-band frequencies. The effects of other parameters are carried out for the output gain.