The inertia effect induced by the motion of heat flow will have a significant impact on the heat transfer, when the heat pulse duration or the device structure has micro-scale characteristics. Based on the thermomass theory, the thermal wave equation is introduced to describe the motion of thermomass, and the generalized thermoelastic dynamic model involved in the thermal inertia is established by combining the constitutive relation of isotropic material. By taking into account the micro-scale characteristics for the transient heat transfer, the one-dimensional problem for the semi-infinite solid with the boundary subject to thermal impact is investigated by an analytic method, where the asymptotic solutions for thermoelastic response are obtained. With these solutions, the propagation of the thermal wave and thermal elastic wave and the distribution of the temperature, displacement and stresses are studied. By comparison with the same predictions of the L-S generalized thermoelasticity, the effect of thermal inertia on the thermal behaviors is revealed. The results show that the spatial thermal inertia induced by the motion of heat flux has an impact on the thermal behaviors, except for the temporal thermal inertia. All the velocities and wavefront locations of thermal wave and thermal elastic wave, and the time of each physical field begin to establish, the peak values of jumps and the intervals of two jumps are influenced by the spatial thermal inertia.