This study examines the impact of sinusoidal time-dependent injection velocities on miscible thermo-viscous fingering instabilities observed in enhanced oil recovery. Linear stability analysis (LSA) and nonlinear simulations (NLS) are used to investigate fingering dynamics, considering parameters such as thermal mobility ratio ( Rθ), solutal mobility ratio ( Rc), Lewis number (Le), and thermal-lag coefficient ( λ ). The LSA employs a quasi-steady state approximation in a transformed self-similar coordinate system, while NLS uses a finite element solver. Two injection scenarios are explored: injection-extraction ( Γ = 2 ) and extraction-injection ( Γ = − 2 ), with fixed periodicity ( T = 100 ). Results show that for unstable solutal and thermal fronts ( Rc > 0 , Rθ > 0 ), increasing Le with fixed λ ≠ 1 leads to more prominent mixing and interfacial length for Γ = 2 compared to constant injection and Γ = − 2 . While for unstable solutal fronts ( Rc > 0 ) and stable thermal fronts ( Rθ < 0 ), increasing Le results in more prominent mixing and interfacial length for Γ = − 2 , except during early diffusion. Thus, when porous media are swept using cold fluid, increasing the Lewis number intensifies the level of flow instability for Γ = − 2 ; whereas when hot fluid is used, the instability enhances for Γ = 2 . Furthermore, it is observed that the high thermal diffusion ( Le ≫ 1 ) and enhanced thermal redistribution between solid and fluid phases ( λ ≪ 1 ) effectively mitigate destabilizing effects associated with positive Rθ, reducing overall instability. Overall, in extraction-injection scenarios, the phenomenon of tip-splitting and coalescence is attenuated, and the channeling regime is observed.