  The consistency condition, which guarantees a well organized small-coupling
asymptotic expansion for the thermodynamics of massless $\phi^4$-theory, is
generalized to any desired order of the perturbative treatment. Based on a
strong conjecture about forbidden two-particle reducible diagrams, this
condition is derived in terms of functions of four-momentum in place of the
common toy mass in previous treatments. It has the form of a set of gap
equations and marks the position in the space of these functions at which the
free energy is extremal.
