Finite temperature matrix theory

We present a way in which the Lorentz invariant canonical partition function for matrix theory as a light-cone formulation of M-theory can be computed. We explicitly show how, when the eleventh dimension is decompactified, the N=1 eleven-dimensional SUGRA partition function appears. We also provide a high temperature expansion which captures some structure of the canonical partition function when interactions amongst D-particles are turned on. The connection with the semi-classical computations thermalizing the open superstrings attached to a D-particle is also clarified through a Born-Oppenheimer approximation. Some ideas about how matrix theory would describe the complementary degrees of freedom of the massless content of eleven-dimensional SUGRA are discussed. Comments on possible connections to black hole physics are also made. (orig.)