By considering the Cattaneo–Christov approach and Buongiorno’s model, the thermal transport model is formulated for the flow of Oldroyd-B nanofluid over a bidirectional stretching surface. The flow profile of Oldroyd-B nanofluid is examined for various physical parameters, and the effects of heat source/sink are also utilized to explore the thermal transport properties subject to thermal relaxation time. Governing mathematical models are developed on the basis of basic laws and presented in the form of Partial differential equations (PDEs). The governing partial differential equations are transformed into ordinary differential equations considering suitable dimensionless transformations. The homotopic method is applied to study the feature of heat and velocity components in fluid flow. The influence of each physical parameter over the thermal and concentration profile is displayed graphemically. It is noticed that thermal transport is decreasing with increment in thermal relaxation time. The mass transfer becomes weak with magnifying values of the stretching strength parameter. Moreover, the larger thermophoretic parameter regulates the heat transfer during fluid flow.