In the existence of a thermal source, this study examines the impacts of thermal stratification on the heat transmission characteristics of magnetohydrodynamic water-based copper/molybdenum disulfide Casson hybrid nanofluid flow across a vertical cylinder which is linearly stretching. A magnetic field with an inclination is applied along the stretched vertical cylinder. The driving forces for the flow are due to the stretched cylinder and natural convection. With appropriate similarity transformations, non-linear ordinary differential equations are obtained from the collection of mathematically modeled partial differential equations. The numerical findings are obtained by utilizing the MATLAB bvp4c approach. The consequence of protuberant factors on the thermal and velocity curves is also studied and is depicted pictorially. The outcomes of the friction drag and the thermal transmission rate are summarized in the table. The important contributions highlight that water-based copper/molybdenum disulfide Casson hybrid nanofluids have superior thermal conductivity than water-based copper Casson nanofluids. The water-based Casson hybrid nanofluid fluid has a noteworthy influence on enhancing thermal procedures. Thermal exchangers, solar power systems, automotive cooling down and precision manufacturing are among their beneficial functions. The friction drag for Casson hybrid nanofluid has been found to improve by up to 32.3% when contrasted to water-based Casson nanofluid. While contrasting the Casson hybrid nanofluid with the Casson nanofluid, the thermal transport rate is increased by almost 6.6%. The rate of thermal transmission at the solid surface is negatively impacted by thermal stratification. This finding has practical implications in the areas of bettering materials for thermal insulation and energy-effective designs for buildings. The outcomes reflect a significant enrichment in the discipline of fluid dynamics and nanofluid research since they offer promising potential for heat transfer optimization in various commercial environments.