[en] We study the equation of state of a strongly interacting theory of relativistic bosons and chiral fermions in the vicinity and above the chiral phase-transition temperature. Our model resembles presently used low-energy models of QCD in many ways, but its simplicity allows us to study systematically various approximation schemes by means of a derivative expansion. In particular, we compare the results for the phase-transition temperature, equation of state, and the thermal mass of the scalar fields obtained in various approximations. We find that the large-N_c approximation, being the zeroth order of our approximation, deviates significantly from approximation schemes in which effects of (pseudo-) Goldstone modes have been taken into account, even at high temperatures and even if we allow for a finite explicit symmetry breaking. The important role of the (pseudo-) Goldstone modes is also manifested in the phenomenon of 'local order' which is missing in large-N_c studies.