We construct perturbatively a class of charged black hole solutions in type
0A string theory with higher derivative terms. They have extremal limit, where
the solution interpolates smoothly between near horizon AdS_2 geometry and the
asymptotic linear dilaton geometry. We compute the free energy and the entropy
of those solution using various methods. In particular, we show that there is
no correction in the leading term of the free energy in the large charge limit.
This supports the duality of the type 0A strings on the extremal black hole and
the 0A matrix model in which the tree level free energy is exact without any
alpha' corrections.Comment: Latex, 19 page