  We consider N=2 supergravity in four dimensions with small R^2 curvature
corrections. We construct large charge non-extremal black hole solutions in all
space, with either a supersymmetric or a non-supersymmetric extremal limit, and
analyze their thermodynamic properties. This generalizes some of the extremal
solutions presented in [arXiv:0902.0831]. The indexed entropy of the
non-extremal extension of the supersymmetric black hole, has the form of the
extremal entropy, with the charges replaced by a function of the charges, the
moduli at infinity and the non-extremality parameter. This is the same behavior
as in the case without R^2-terms.
