The present attempt is made to report the flow regime characteristics of tangent hyperbolic fluid when both the magnetic field and heat generation effects are taken into account. The flow narrating differential equations subject to thermally stratified medium are transformed into a system of nonlinear ordinary differential equations. A computational algorithm is developed to offer a numerical solution of the flow problem. The physical outcomes against flow controlling parameters namely, curvature parameter, Weissenberg number, power law index, thermal stratification, heat generation and Prandtl number are discussed and illustrated via graphs and tables. The outcomes are certified by providing comparison with existing literature in a limiting sense. Keywords: Tangent hyperbolic fluid, MHD, Thermal stratification, Heat generation, Shooting method