The present research discusses a generalized thermoelastic model with variable thermal material properties and
derivatives based on memory. Based on this new model, an infinitely long homogeneous, isotropic elastic body with a cylindrical
hole is analyzed for thermal behavior analysis. The governing equations are deduced by the application of the principle of
memory-dependent derivatives and the generalized law on heat conduction. In a numerical form, the governing differential
equations are solved utilizing the Laplace transform technique. Numerical calculations are shown in graphs to explain the effects
of the thermal variable material properties and memory dependent derivatives. In addition, the response of the cylindrical hole is
studied through the effects of many parameters such as time delay, the kernel function and boundary conditions. The results
obtained with those from previous literature are finally verified