Electrohydrodynamic pumps, as a representative type of nonmechanical pump, have received significant research attention due to their inherent advantages of having no moving parts and low power consumption. In particular, the planar charge injection pump has exhibited superior fluid driving performance, making it highly promising for applications in microscale flow driving and chip cooling. A sandwich structure pump with multiple pairs of planar interdigitated electrodes is numerically studied in this paper. The interaction of the flow, thermal, and electric fields is analyzed using the lattice Boltzmann method under different pump configurations, governing parameters, and convection mechanisms. The results reveal that the geometric configurations of the planar interdigitated electrodes have direct effects on the pumping performance and heat transfer rate. Specifically, an optimal configuration is achieved when the width of the collector is twice that of the emitter under two-pair electrode simulation conditions. More interestingly, competition between electric and thermal effects is observed, and the optimal threshold for heat transfer is found at an electric Rayleigh number of T = 300 for the considered cases. Finally, the interaction of the electric and thermal fields induces periodic oscillations. The single-vortex mechanism exhibits the longest oscillation period and inhibits heat transfer, while the multi-vortex mechanism has the shortest oscillation period and enhances heat transfer.