  We consider a generic classical many particle system described by an
autonomous Hamiltonian $H(x^{_1},...,x^{_{N+2}})$ which, in addition, has a
conserved quantity $V(x^{_1},...,x^{_{N+2}})=v$, so that the Poisson bracket
$\{H,V \}$ vanishes. We derive in detail the microcanonical expressions for
entropy and temperature. We show that both of these quantities depend on
multidimensional integrals over submanifolds given by the intersection of the
constant energy hypersurfaces with those defined by
$V(x^{_1},...,x^{_{N+2}})=v$. We show that temperature and higher order
derivatives of entropy are microcanonical observable that, under the hypothesis
of ergodicity, can be calculated as time averages of suitable functions. We
derive the explicit expression of the function that gives the temperature.
