To assess diffusion's importance, the temperature distribution in a cylindrical reactor is derived for a coolant with uniform properties and velocity, taking into account both radial and axial diffusion, for a cosine-J0 power distribution. The fractional temperature rise of the coolant is found to be where Ε(z) = [sin(z) + sin(Ζ)]/2 sin(Ζ), z= π x/2Η′, x is the axial distance from the core center, -Η and Η′ are the core half-height and extrapolated half-height, -Η≤x≤Η; Fn = 1/J0(Pn)·[(Pn/2.405P)2-10, J1(Pn) = 0, P= R/R′ = core radius/extrapolated radius, ρ = r/R, r = radial distance from axis, 0≤r≤R;an = = βnH/Z, 2 Αβn + 1 =[1+4ΑΒ(Pn/R)2]½ , Α = axial diffusivity /u, Β = radial diffusivity /u, u = coolant axial velocity, and The expression is evaluated for a variety of values for all the parameters, and the results are discussed analytically and presented in tables and graphs. The effect is dependent upon the relative size of the diffusion eddies in comparison with the dimensions of the reactor. The eddy diffusivity is proportional to the size of the particles in the bed and is about ten times larger axially than radially. A small core with large fuel particles will be affected by eddy diffusion, thereby reducing hot spots, but a large core with small particles will not. For a core 8 ft in diameter cooled by sodium flowing at 2 ft/sec, the effect is perceptible with 2-in. particles, but not with 0.2-in. particles.