<p>In this study, a non-isothermal chromatographic model is formulated and analyzed by coupling a Tri-Langmuir adsorption isotherm with the Lumped Kinetic Model (LKM). The proposed framework accounts for axial dispersion, finite mass-transfer resistance, and thermal effects arising during adsorption, enabling a more realistic description of the transport and separation of multiple chemical species in a packed chromatographic column. The resulting system of governing equations is solved numerically using the Runge–Kutta Local Discontinuous Galerkin (RK-LDG) method, which is particularly well suited for handling steep concentration and temperature gradients. Different numerical simulations were conducted to examine the effects of temperature, injection conditions, and flow rate as well as multi-site adsorption on chromatographic peaks. It has been shown that the Tri-Langmuir isotherm is a more accurate model of multi-component and nonlinear adsorption than the linear or the Bi-Langmuir model. The objective of this work is that accurate separation of complex mixtures requires careful consideration of both temperature variations and multi-site adsorption effects. Simplified assumptions, such as isothermal operation or single-site binding, can lead to significant deviations in predicted chromatographic behavior. By explicitly accounting for these factors, the proposed model provides a more reliable description of column dynamics and offers a practical framework for improving the design and optimization of chromatographic separation processes in demanding applications.</p>