A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.