  The perfect fluid solutions admitting a group G$_3$ of isometries acting on
orbits S$_2$ whose curvature has a gradient which is tangent to the fluid flow
(T-models) are studied from a thermodynamic approach. All the admissible
thermodynamic schemes are obtained, and the solutions compatible with the
generic ideal gas equation of state are studied in detail. The possible
physical interpretation of some previously known T-models is also analyzed.
