  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 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 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 ${\mathbb R}^9\otimes{mathbb T}^2$.
Alternatively we argue that any finite temperature can be introduced in the
framework of membrane thermodynamics.
