  We present the details of a mean-field approximation scheme for the quantum
mechanics of N D0-branes at finite temperature. The approximation can be
applied at strong 't Hooft coupling. We find that the resulting entropy is in
good agreement with the Bekenstein-Hawking entropy of a ten-dimensional
non-extremal black hole with 0-brane charge. This result is in accord with the
duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We
study the spectrum of single-string excitations within the quantum mechanics,
and find evidence for a clear separation between light and heavy degrees of
freedom. We also present a way of identifying the black hole horizon.
