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In this paper, a fluid–structure interaction problem, forced heat transfer from the circular cylinder forced to oscillate in an elliptical path in an incompressible fluid flow, is numerically simulated. In-house developed code used for the simulations is based on Arbitrary Lagrangian–Eulerian formulation with Harten Lax and van Leer with contact for artificial compressibility method. The mesh's dynamic movement was taken care of by actually moving the mesh using radial basis function-based interpolation. The Harten Lax and van Leer with contact Riemann scheme, developed for incompressible flows, was used to evaluate convective fluxes in artificial compressibility formulation. High order accuracy is achieved over an unstructured data structure using solution-dependent weighted least squares-based gradient calculations. The laminar unsteady incompressible flow is mainly affected by Reynolds number, Re, Prandtl number, Pr, the amplitude of cylinder oscillation, i.e., major and minor radius of the elliptical oscillating path and cylinder vibrating frequency. In the paper, these parameters are varied as Re = 100, 150, 200; the elliptical oscillation path's major and minor radius varies from 0.1 D to 0.6D (D is the cylinder diameter); and cylinder vibrating frequency ratio is 0.5 to 3.0. The characteristics of forced elliptical motion are different from that of transversely oscillating or streamline oscillating cylinder cases. The heat transfer increases with the oscillation amplitude and vibrating frequency ratio for the given Reynolds number and Prandtl number. Cylinder oscillating with a higher transverse radius shows a higher increase in heat transfer rate than the higher in-line oscillation amplitude. A maximum 40% increase in Nusselt number is obtained for the highest value of Reynolds number, 200, oscillation amplitude 0.6D and frequency ratio of 3. The detailed results are presented along with a comparison with the literature results. [ABSTRACT FROM AUTHOR]