Capillary osmotic (CO) transport of electrolytic liquids driven by a concentration gradient through charged nanopores is fundamentally important in many biological and industrial systems. Conventional models describing ionic transport in micro/nanofluidic systems often consider ions as point charges consistent with the mean-field theories. In nanofluidic geometries and at high electrolyte concentrations, finite ionic size, also known as the steric effect, significantly modulates the underlying transport, and classical theories fail to describe the transport phenomena accurately. To account for the steric effects on ionic transport in this endeavor, we modify the Nernst–Planck equation by incorporating an additional electrochemical potential using the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model, which treats ions as hard spheres and is compared with the lattice-based Bikerman model. We consider three monovalent electrolytic (namely, LiCl, NaCl, and KCl) solutions with increasing cation hydrated radius, respectively, to investigate the steric effect modulated transport through the nanopore. Our analysis shows that finite ion size reduces counterion accumulation near the pore wall, with the BMCSL model predicting stronger exclusion compared to the Bikerman model. This reduced screening enhances the electrical double layer (EDL) potential magnitude and strengthens the induced axial electric field, which, in turn, augments the flow velocity relative to point-charge predictions. Our study also investigates the influence of a temperature gradient across the reservoirs in addition to the concentration gradient, thereby introducing thermodiffusion effects. The presence of thermodiffusion is found to diminish wall screening and enhance both the EDL potential and electric field strength, leading to a trigger in the net throughput. We believe that the insights gained from the present study on the temperature gradient-assisted transport of ionic liquids hold significant potential for advancing the design of next-generation temperature-sensitive biosensors and nanofluidic devices.