  Using the quantum Hamiltonian for a gravitational system with boundary, we
find the partition function and derive the resulting thermodynamics. The
Hamiltonian is the boundary term required by functional differentiability of
the action for Lorentzian general relativity. In this model, states of quantum
geometry are represented by spin networks. We show that the statistical
mechanics of the model reduces to that of a simple non-interacting gas of
particles with spin. Using both canonical and grand canonical descriptions, we
investigate two temperature regimes determined by the fundamental constant in
the theory, m. In the high temperature limit (kT > m), the model is
thermodynamically stable. For low temperatures (kT < m) and for macroscopic
areas of the bounding surface, the entropy is proportional to area (with
logarithmic correction), providing a simple derivation of the
Bekenstein-Hawking result. By comparing our results to known semiclassical
relations we are able to fix the fundamental scale. Also in the low
temperature, macroscopic limit, the quantum geometry on the boundary forms a
`condensate' in the lowest energy level (j=1/2).
