In this paper, we discuss the non-thermal distribution, the energy density and entropy increase of a massless particle gas in the Multi-dimensional phase of universe. Starting from the assumption that the distribution of particle number be invariant during the inflation, and in the approximate condition that the initial temperature T0 = β0-1 1/2a20-1 (D is the dimension of the extra space and a20 is the scale of the extra space befor inflation), we calculate the ratio of the total entropy St at the ending of the Multi-dimensional phase to the corresponding quantity S0 in the initial stage, which has the same order of magnitude as the ratio of T0a20 to Tfa2f (Tf is the temperature just as the universe enters the ordinary phase and a2f is the stable scale of the extra space. Planck unit, h =c = kB=G= 1, is used throughout ).