  The early universe is dominated by phenomena at high temperatures. The
thermal effects decrease during evolution of the universe. However there are
some phenomena, such as processes inside stars and black holes, where the role
of the temperature is important. Study of processes involving gravitons at
finite temperature is a viable means to understand gravitational processes in
the universe. Using the Thermo Field Dynamics formalism transition amplitudes
involving gravitons and fermions at finite temperature are calculated. In this
approach our results consist of two parts: one corresponding to the zero
temperature part and the other corresponding to a temperature dependent part.
