Laminar forced convection flow past an in-line elliptical cylinder array with inclination is simulated using the finite element method. The inclination of the elliptical cylinders is increased with the number of the cylinder in the array, 0 deg for the first cylinder and 90 deg for the last cylinder. The global objective of this research is to enhance the heat transfer out of the cylinders. A parametric study of heat exchanges between the cylinders and flow (expressed by the Nusselt number) is reported for Reynolds numbers between 125 and 1000, while the Prandtl number is fixed at 0.71. The results are compared with an elliptical cylinder array without inclination to assess the heat transfer enhancement. The problem is solved as transient, and a vortex shedding phenomenon is reported. The results indicated that the Reynolds number has a significant effect on the heat transfer out of the cylinders, and the inclination of the elliptical cylinders enhances heat transfer rate up to 238.59%, but pressure drop is increased as high as 700%. Also, skin-friction coefficient along the five cylinders’ perimeter, plots of the velocity flow field, and temperature contours are presented.