  We consider perturbative solutions to the classical field equations coming
from a quadratic gravitational lagrangian in four dimensions. We study the
charged, spherically symmetric black hole and explicitly give corrections up to
third order (in the coupling constant $\beta$ multiplying the
$R_{\mu\nu}R^{\mu\nu}$ term) to the Reissner--Nordstr\"om hole metric. We
consider the thermodynamics of such black holes, in particular, we compute
explicitly its temperature and entropy--area relation which deviates from the
usual $S=A/4$ expression.
