  We perform an exact computation of the grand partition function of a model of
confined quarks at arbitrary temperatures and quark chemical potentials. The
model is inspired by a version of QCD where the perturbative BRST symmetry is
broken in the infrared, while perturbative QCD is recovered in the ultraviolet.
The theory leads, even at tree level, to a quark mass function compatible with
nonperturbative analyses of lattice simulations and Dyson-Schwinger equations.
In spite of being defined at tree level, the model produces a non-trivial and
stable thermodynamic behaviour at arbitrary values of temperature or chemical
potential. Results for the pressure and the trace anomaly as a function of
temperature qualitatively resemble those of non-perturbative interactions as
observed in lattice simulations. The cold and dense thermodynamics is also
contains non-trivial features, being unlike a gas of free massive particles.
