This study investigates the unsteady, two-dimensional flow and heat transfer past a sinusoidally rotating circular cylinder, subject to linear shear. A higher order compact (HOC) finite difference scheme is used to solve the governing Navier-Stokes equations coupled with the energy equation on a non-uniform grid in polar coordinates. The hydrodynamic and thermal features of the flow are mainly influenced by the shear rate (K), Reynolds number (Re), Prandtl number (P r) and the cylinder oscillation parameters i.e. maximum angular velocity (am), the frequency ratio (fr). The simulations are performed for Re = 100, P r = 0.5 - 1.0, K ? [0.0, 0.15] and am ? [0.5, 2.0]. The numerical scheme is validated with the existing literature studies. Partial and full vortex suppression is observed for certain values of shear parameter K. The connection between heat transfer and vortex shedding phenomenon is examined where a pronounced increase in the heat transfer is observed for certain values of oscillation parameter, relative to the non-shear flow case.