The Penrose inequality estimates the lower bound of the mass of a black hole
in terms of the area of its horizon. This bound is relatively loose for
extremal or near extremal black holes. We propose a new Penrose-like inequality
for static black holes involving the mass, area of the black hole event horizon
and temperature. Our inequality includes the Penrose inequality as its
corollary, and it is saturated by both the Schwarzschild and
Reissner-Nordstr\”om black holes. In the spherically-symmetric case, we prove
this new inequality by assuming both the null and trace energy conditions.