  The kernel of the evolution equation is used to build a mathematical theory
of thermal phenomena of gaseous and condensed matter. The group velocity of
sound and the molar density are proposed to be its two thermal variables that
replace the over-complete set of temperature, pressure and volume. The defining
constants of the New SI (2019) of physical units are used to form a
dimensionless variable of the new geometrical thermal theory. The dimensionless
thermal sum generates, by the variation principle, equations on physical
observables. Energy and entropy are neither defined nor needed in the present
formalism. The molar specific heat is derived and its temperature dependence is
verified with the experimental data for mono-atomic gases. Critique of the
postulates and notions of traditional statistical thermodynamics is given.
