  We develop an approximation scheme for the quantum mechanics of N D0-branes
at finite temperature in the 't Hooft large-N limit. The entropy of the quantum
mechanics calculated using this approximation agrees well 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. Our approximation scheme
provides a model for the density matrix which describes a black hole in the
strongly-coupled quantum mechanics.
