  Strong $\gamma$-ray emission from cocoons of young radio galaxies is newly
predicted. Considering the process of adiabatic injection of the shock
dissipation energy and mass of the relativistic jet in active nuclei (AGNs)
into the cocoon, while assuming thermalizing electron plasma interactions, we
find that the thermal electron temperature of the cocoon is typically predicted
in $\sim$MeV, which is determined only by the bulk Lorentz factor of the
relativistic jet. Together with the time-dependent dynamics of the cocoon
expansion, we find that young cocoons can yield thermal bremsstrahlung
emissions at energies $\sim$ MeV.
