  The effective compton cross section in a non-degenerate
plasma($n\ll\{\frac{(kT/c)^{2}+2mkT}{h^{2}}\}^{^{3/2}}$) is investigated in a
wide range of temperatures. The results show a decreasing behavior with
temperature especially for $kT\gg m_{e}c^{2}$. The $may be important in
phenomena like accretion discs or ultra-relativistic blast waves in GRB models,
where the emitted radiation has to pass through a medium containing high energy
electrons.
