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 qu
antum mechanics calculated using this: approximation agrees well with the B
ekenstein-Hawking entropy of a ten-dimensional nonextremal bind, hole with
0-brane charge. This result is in accordance with the duality conjectured b
y Itzhaki, Maldacena, Sonnenschein, and Yankielowicz [Phys. Rev. D 58, 0460
04 (1998)]. Our approximation scheme provides a model for the density matri
x which describes a black hole in the strongly coupled quantum mechanics.