The flux distribution of a pulsed neutron experiment is expanded in terms of eigenfunctions with respect to both energy and space. The diffusion cooling constant is given exactly in terms of matrix elements with respect to these eigenfunctions. These matrix elements are evaluated for the special case of a heavy gas moderator. It is also possible to develop the theory for heterogeneous assemblies. The interaction of the cell and the assembly buckling in these structures is described and the diffusion cooling effect is considered. In addition to the normal diffusion cooling effect, a second cooling effect appears which is due to the neutrons which diffuse into the lumped absorbers.