The "basketball diagram" is a three-loop vacuum diagram for a scalar field
theory that cannot be expressed in terms of one-loop diagrams. We calculate
this diagram for a massive scalar field at nonzero temperature, reducing i
t to expressions involving three-dimensional integrals that can be easily e
valuated numerically. We use this result to calculate the foe energy for a
massive scalar field with a phi(4) interaction to three-loop order.