We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T H . The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology [Formula: see text]. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.