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The terahertz (THz) propagation in real tissues causes heating as with any other electromagnetic radiation propagation. A finite-element (FE) model that provides numerical solutions to the heat conduction equation coupled with realistic models of tissues is employed in this study to compute the temperature raise due to THz propagation. The results indicate that the temperature raise is dependent on the tissue type and is highly localized. The developed FE model was validated through obtaining solutions for the steady-state case and showing that they were in good agreement with the analytical solutions. These types of models can also enable computation of specific absorption rates, which are very critical in planning/setting up experiments involving biological tissues.