In present work, Green–Nagdhi (type III) thermoelastic half-space under hydrostatic initial stress is taken into consideration. The thermoelastic half-space is subjected to a mechani cal load acting on the free surface along the normal direction. The thermal conductivity of the medium is believed to be temperature-dependent and to vary linearly. The formulas for the temperature distribution, stress, and displacement components are obtained by apply ing the normal mode analysis approach. Analytical evaluation is performed on the physi cal characteristics exhibiting temperature-dependent thermal conductivity. The influence of temperature dependency and hydrostatic starting stress on these physical parameters is then illustrated graphically by evaluating these physical values numerically using algorithms cre ated in MATLAB 7.0