In this work, a general finite element model is proposed to analyze transient phenomena in thermoelastic half-space filled with an elastic material, which has constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in IMA J. Appl. Math. 71(3):383–390, 2006). A linear temperature ramping function is used to more realistically model thermal loading of the half-space surface. The medium is assumed initially quiescent. A finite element scheme is presented for the high accuracy numerical purpose. The numerical solutions of the non-dimensional governing partial differential equations of the problem have been shown graphically and some comparisons have been shown in figures to estimate the effect of the ramping parameter of heating and the parameter of two-temperature.