Some n-dimensional variable coefficient linear second order degenerate parabolic equations were discussed. Under certain degeneration conditions, the Harnack property for nonnegative strong solution of degenerate parabolic equations was obtained by parabolic maximum principle and inequality estimates. The obtained conclusion extended the Harnack inequality for uniformly parabolic equations to a class of degenerate parabolic equations. An interpretation was given to this Harnack inequality in terms of heat conduction property of three-dimensional parabolic equations.