<p>This study investigates thermal energy transport in a microscale heterogeneous thermoelectric system. It is common knowledge that a finite time is needed to complete any physical interactions in materials. The two most essential factors in thermal sciences are the heat flux vector and temperature gradient, which occur at different times during the transport process. This leads to the concept of thermal lagging. The dual-phase-lag model is utilized to determine the interaction of these two factors, as mentioned earlier, by using two relaxation constants, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\tau }_{T}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mi>T</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\tau }_{q}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation>, to explore the lagging behavior. The magnitudes of these two constants play an essential role in energy transport in microscale and nanoscale thermal systems. A high-order hyperbolic partial differential equation is utilized to determine the cause-and-effect interaction for a particular pair of relaxation constants. Ultimately, one needs to solve a coupled, but moderately simple, system of finite difference equations that involves the temperature and heat flux simultaneously. The effects of relaxation constants and temperature-dependent material properties in semiconductor thermoelements are thoroughly examined. The microscale heat transport phenomenon plays a significant role in thermal management technology. The study confirmed that the dual-phase-lag model is an appropriate design tool for engineers in the thermoelectric industry.</p>