  We show that the temperature of a diffusing fluid with the diffusion constant
\kappa^{2} in an expanding universe approaches a constant limit T=\kappa^{2}/H
in its final de Sitter stage characterized by the horizon 1/H determined by the
Hubble constant. If de Sitter surface temperature in the final equilibrium
state coincides with the fluid temperature then the cosmological constant
\Lambda=3H^{2}=6\pi\kappa^{2}.
