Abstract Based on the coupled Boltzmann equations for phonons and localized tunneling systems non-linear field equations for phonon energy, tunneling states energy and phonon momentum have been derived. It is shown that the solution of these hyperbolic field equations for given boundary and initial values of heat-pulse experiments are in excellent agreement with new experimental data obtained in vitreous silica at temperatures down to 15 mK. The temperature profiles of heat-pulse experiments were measured by in situ capacitance thermometry. This represents a direct method to determine the temperature by recording the polarization of tunneling systems in glasses. In the thermodynamic field theory the specific heat of glasses is not explicitely time-dependent, and its complete temperature dependence can be obtained by evaluating one temperature versus time profile, only.