  We perform a direct test of the gauge-gravity duality associated with the
system of N D0-branes in type IIA superstring theory at finite temperature.
Based on the fact that higher derivative corrections to the type IIA
supergravity action start at the order of \alpha'^3, we derive the internal
energy in expansion around infinite 't Hooft coupling up to the subleading term
with one unknown coefficient. The power of the subleading term is shown to be
nicely reproduced by the Monte Carlo data obtained nonperturbatively on the
gauge theory side at finite but large effective (dimensionless) 't Hooft
coupling constant. This suggests, in particular, that the open strings attached
to the D0-branes provide the microscopic origin of the black hole
thermodynamics of the dual geometry including \alpha' corrections. The
coefficient of the subleading term extracted from the fit to the Monte Carlo
data provides a prediction for the gravity side, which can be checked once the
complete form of the O(\alpha'^3) corrections to the supergravity action is
obtained.
