Relying on the Luttinger-Ward theorem we derive a thermodynamically se
lf-consistent and scale-independent approximation of the thermodynamic
potential for the scalar phi(4)-theory in the tadpole approximation.
With certain approximations the presented approach can be extended to
quantum chromodynamics (QCD) and it gives support to parametrize the r
esults of QCD lattice calculations by suitably modified ideal-gas expr
essions.