  A family of parabolic Szekeres-Szafron class II solutions in local thermal
equilibrium is studied and their associated thermodynamics are obtained. The
subfamily with the hydrodynamic behavior of a generic ideal gas (defined by the
equation of state $p = k n \Theta$) results to be an inhomogeneous
generalization of flat FLRW $\gamma$-law models. Three significative
interpretations that follow on from the choice of three specific thermodynamic
schemes are analyzed in depth. First, the generic ideal gas in local thermal
equilibrium; this interpretation leads to an inhomogeneous temperature
$\Theta$. Second, the thermodynamics with homogeneous temperature considered by
Lima and Tiomno (CQG 6 1989). And third, a new model having exactly the
homogeneous temperature of the FLRW limit. It is shown that the three models
above fulfill the necessary macroscopic requirements for physical reality
(positivity of matter density and temperature, energy conditions and
compressibility conditions) in wide domains of the spacetime.
