  The partition function of composite bosons ("cobosons" for short) is
calculated in the canonical ensemble, with the Pauli exclusion principle
between their fermionic components included in an exact way through the finite
temperature many-body formalism for composite quantum particles we recently
developed. To physically understand the very compact result we obtain, we first
present a diagrammatic approach to the partition function of $N$ elementary
bosons. We then show how to extend this approach to cobosons with Pauli
blocking and interaction between their fermions. These diagrams provide deep
insights on the structure of a coboson condensate, paving the way toward the
determination of the critical parameters for their quantum condensation.
