  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.
