It is known that Fourier’s heat equation which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte was proved that such process can be describe by Heaviside’s telegraph equation. In this paper has been shown that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that equation of heat conduction with finite velocity propagation of the thermal disturbance, can be obtained as solution of one variational problem.