In this article, we investigate the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolicnon-Newtonian fluid from a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Prandtl number (Pr), Biot number (γ), and dimensionless local suction parameter(ξ)on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is found that velocity, Skin friction and Nusselt number (heat transfer rate) are reduced with increasing Weissenberg number (We), whereas, temperature is enhanced. Increasing power law index (n) enhances velocity and Nusselt number (heat transfer rate) but temperature and Skin friction decrease. An increase in the Biot number (γ) is observed to enhance velocity, temperature, local skin friction and Nusselt number. An increasing Prandtl number, Pr, is found to decrease both velocity, temperature and skin friction but elevates heat transfer rate (Nusselt number). The study is relevant to chemical materials processing applications.