In astrophysical jets observed in active galactic nuclei and in microquasars, the energy exchange rate by Coulomb collision is insufficient for thermal equilibrium between ions and electrons. Therefore, it is necessary to consider the difference between the ion temperature and the electron temperature. We present the results of two-temperature magnetohydrodynamics(MHD) simulations to demonstrate the effects of Coulomb coupling. It is assumed that the thermal dissipation heats only ions. We find that the ion and electron temperatures are separated through shocks. Since the ion entropy is increased by energy dissipation at shocks and the Coulomb collisions are inefficient, electron temperature becomes about 10 times lower than the ion temperature in the hotspot ahead of the jet terminal shock. In the cocoon, electron temperature decreases by gas mixing between high temperature cocoon gas and low temperature shocked-ambient gas even when we neglect radiative cooling, but electrons can be heated through collisions with ions. Radiation intensity maps are produced by post processing numerical results. Distributions of the thermal bremsstrahlung radiation computed from electron temperature have bright filament and cavity around the jet terminal shock.propagation of light supersonic jets, which exhibited the basic structures of jets such as a bow shock, a terminal shock (a reverse shock), internal shocks, and a cocoon. Recently, jet propagation and its feedback to inter cluster medium has been studied in realistic environments of galaxy cluster by Guo et al. [6,7]. The spacial variation of the propagation velocity of the jet has been reported by analytical methods (e.g., [8,9]) and by numerical simulations (e.g., [10]).The magnetic field structure of jets has been studied using polarized radiation. Faraday tomography have revealed that jets in 3C273 and SS433/W50 [11,12] have a helical magnetic field. The effects of magnetic fields on the jet dynamics have been examined for both non-relativistic and relativistic jets assuming axisymmetry [13][14][15]. In three-dimensional calculations, jets develop current-driven kink instability (m = 1) [16,17]. In addition, some studies compared numerical results with observations [18][19][20].Previous studies, however, did not focus on thermal non-equilibrium between ions and electrons in optically thin plasmas. When the relaxation time of ions and electrons by Coulomb collisions is longer than the dynamical time, the electron temperature can be lower than the ion temperature partly because electrons are cooled by radiation, and partly because shock waves primarily heat ions. Therefore, the electron temperature becomes lower than the ion temperature under such circumstances [21,22]. Such a two-temperature plasma has been studied extensively in the context of optically thin hot accretion flows in galactic black hole candidates (Shapiro, Lightman and Eardley [23]) and in the jet launching region in low luminosity active galactic nucleis (AGNs). Ressler et al. [24] and Sadowski et al. [2...