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The nonlinear simulation of interfacial instabilities in miscible displacements in porous media often requires sophisticated numerical algorithms as well as very fine spatial and temporal resolutions. In this study, Hartley transform based pseudo-spectral method is used to simulate time evolution of thermoviscous fingers in rectilinear geometry. The problem is formulated using continuity equation, Darcy's law, and volume-averaged forms of convection-diffusion equation for mass and energy balance. The numerical code is validated against established results for isothermal displacements. The effects of exponential dependence of viscosity on concentration and temperature, Lewis number, and porosity on the stability of the thermo-viscous flow are examined. It has been generally observed that at practical values of porosity and Lewis number, the thermal front always lags behind the fluid front and the instability is dominated by the viscosity variation due to concentration.