The damping of the nuclear shell effect with excitation energy has been measured through an analysis of the neutron spectra following the triton transfer in the (7)Li induced reaction on (205)Tl. The measured neutron spectra demonstrate the expected large shell correction energy for the nuclei in the vicinity of doubly magic (208)Pb and a small value around (184)W. A quantitative extraction of the allowed values of the damping parameter γ, along with those for the asymptotic nuclear level density parameter ã, has been made for the first time.