  We present the results of two-temperature magnetohydrodynamic simulations of
the propagation of sub-relativistic jets of active galactic nuclei. The
dependence of the electron and ion temperature distributions on the fraction of
electron heating fe at the shock front is studied for fe=0, 0.05, and 0.2.
Numerical results indicate that in sub-relativistic, rarefied jets, the jet
plasma crossing the terminal shock forms a hot, two-temperature plasma in which
the ion temperature is higher than the electron temperature. The
two-temperature plasma expands and forms a backflow referred to as a cocoon, in
which the ion temperature remains higher than the electron temperature for
longer than 100 Myr. Electrons in the cocoon are continuously heated by ions
through Coulomb collisions, and the electron temperature thus remains at Te >
10^9 K in the cocoon. X-ray emissions from the cocoon are weak because the
electron number density is low. Meanwhile, soft X-rays are emitted from the
shocked intracluster medium surrounding the cocoon. Mixing of the jet plasma
and the shocked intracluster medium through the Kelvin--Helmholtz instability
at the interface enhances X-ray emissions around the contact discontinuity
between the cocoon and shocked intracluster medium.
