The three-dimensional coupled quasi-static problem of linear thermoelasticity is presented. The concept is based on a spatial extension of a region occupied by the considered body and on spatial formulation of a new fictitious load. All the outside objects are termed here fictitious ones. The solution of the initial-space value problem includes fictitious displacement-temperature components. Capacity values of approximate fictitious components are calculated from a boundary condition contracted to the finite time interval. The approximate solution to the primary thermoelastic problem is obtained by contracting in space the approximate solution to the initial-space value problem. It enables us to determine the thermoelastic flow.