We investigate evolution of the intracluster medium (ICM), considering the relaxation process between the ions and electrons. According to the standard scenario of structure formation, ICM is heated by the shock in the accretion flow to the gravitational potential well of the dark halo. The shock primarily heats the ions because the kinetic energy of an ion entering the shock is larger than that of an electron by the ratio of masses. Then the electrons and ions exchange the energy through coulomb collisions and reach the equilibrium. From simple order estimation we find that the region where the electron temperature is considerably lower than the ion temperature spreads out on a Mpc scale. We then calculate the ion and electron temperature profiles by combining the adiabatic model of two-temperature plasma by Fox & Loeb (1997) with spherically symmetric N-body and hydrodynamic simulations based on three different cosmological models. It is found that the electron temperature is about a half of the mean temperature at radii $\sim$ 1 Mpc. This could lead to an about 50 % underestimation in the total mass contained within $\sim$ 1 Mpc when the electron temperature profiles are used. The polytropic indices of the electron temperature profiles are $\simeq 1.5$ whereas those of mean temperature $\simeq 1.3$ for $r \geq 1$ Mpc. This result is consistent both with the X-ray observations on electron temperature profiles and with some theoretical and numerical predictions about mean temperature profiles.

20 pages with 6 figures. Accepted for publication in ApJ