Kirchhoff's type formula for a solution of a central system of field equations of thermoelasticity with finite wave speeds is established in the paper. The solution of the system (φ, θ), where φ and θ denote the thermoelastic displacement potential and temperature respectively, is expressed by surface integrals over the boundary of a thermoelastic solid whose kernels have the form of infinite series involving Bessel functions. Application of the formula to reduce the solution of an initial-boundary problem to that of a vector Fredholm integral equation of the first kind is outlined.