<p>This study examines the three-dimensional heat transfer and flow characteristics of a Casson fluid over an exponentially stretching sheet, a scenario of interest for various industrial and engineering applications. The mathematical model consists of nonlinear partial differential equations that describe fluid motion and heat transfer, which are then transformed into a system of coupled ordinary differential equations using appropriate similarity transformations. These equations account for the non-Newtonian properties of the Casson fluid, along with the effects of exponential stretching, variations in thermal conductivity, and convective boundary conditions. To solve the resulting system, both the Hermite wavelet series collocation method and the shooting method with RKF-45 are employed, ensuring high accuracy and computational efficiency. The solutions are validated by comparing them with existing numerical and analytical results, showing excellent agreement. Various key physical parameters, including the Casson fluid parameter, Prandtl number, and stretching rate, are varied to assess their influence on velocity profiles, temperature distributions, skin friction, and heat transfer rates. The results reveal that the Casson parameter has a significant effect on the fluid's velocity and temperature fields, while exponential stretching increases the thermal boundary layer thickness. These findings offer valuable insights for optimizing processes involving non-Newtonian fluids and complex stretching surfaces.</p>