Miscible non-isothermal flow displacements in homogeneous porous media are modeled and analyzed in flows that involve step-profile velocities that alternate between injection and extraction. The viscosity is assumed to vary with both the concentration and the temperature. The flow is governed by the continuity equation, Darcy's law and the convection-diffusion equations for the concentration and temperature with the assumption of thermal equilibrium. The problem is formulated and solved numerically using a combination of the highly accurate spectral-methods based on the Hartley's transform and the finite-difference technique. Non-linear simulations were carried for a variety of parameters to analyse the effects of the time-dependence of the injection velocity on both the solutal and the thermal front. It is found that for the same net flow rate, time-dependent injections affect not only the solutal front but also the thermal from which can become unstable under time-dependent scenarios when it is known to be stable for flows with a constant injection velocity. The results of this study will be used to improve our understanding of the coupling between heat and mass transfer in flows in porous media and to optimize a variety of non-isothermal flow displacements.