This study investigates the magnetohydrodynamic flow and heat transfer between two parallel disks, considering suction and injection effects at the disks. The governing equations describing the flow and thermal transport are derived based on the principles of mass, momentum and energy conservation for an electrically conducting fluid. As the governing partial differential equations are highly nonlinear, similarity transformations are applied to transform them into coupled ordinary differential equations. Numerical techniques, namely the Hermite wavelet method and Differential transformation technique, are then employed to solve the transformed equations. Parametric effects of several influential parameters such as the Prandtl number, squeeze number, Hartmann number, suction/blowing parameter and thermophoresis parameter on the velocity and temperature profiles are systematically analyzed. Comparisons are made with previous findings in the literature. The results indicate significant dependence of flow behavior and heat transfer on the governing parameters. Velocity and temperature distributions in the boundary layer are presented and discussed in detail. The proposed mathematical model and numerical approach provide useful insights into heat transfer characteristics for parallel disk systems and similar engineering applications involving magnetohydrodynamic flows with suction or injection effects.