The main objective of this study is to examine the two-dimensional (2D) oblique Oldroyd-B flow on a stretching heated sheet. The flow governing problem is converted into nonlinear ordinary differential equations through proper scaling transformations. The prevailing set of equations is solved computationally with a tolerance level of $10^{−5}$. The velocity and temperature of a fluid model under consideration are portrayed to discuss the influence of all associated parameters on momentum and thermal characteristics. Heat flux at the wall has been computed numerically and analysed in a physical manner. The results obtained depict a reversed flow region for non-positive values of shear flow components once a free parameter is varied. It is noticed that heat transfer at the wall drops due to a rise in Deborah number $\beta_{1}$ as well as Biot number Bi.