  In this work we determine for the Cattaneo heat propagation system all the
supplementary balance laws (conservation laws) of the same order (zero) as the
system itself and extract the constitutive relations (expression for the
internal energy) dictated by the Entropy Principle. The space of all
supplementary balance laws (having the functional dimension 8) contains four
original balance laws and their deformations depending on 4 functions of
temperature $\theta$ - $\lambda(\theta),K^{A}(\theta),A=1,2,3$. The
requirements of the II law of thermodynamics leads to the exclusion of three of
these functions ($K^A$) and to further restriction to the form of internal
energy. In its final formulation, entropy balance represent the deformation of
the energy balance law by the functional parameter $\lambda (\theta)$.
