A finite difference procedure for heat conduction in elliptical cylinders using heat flow lines was developed. This method reduces the elliptical heat transfer problem from 3 to 2-dimensional for finite length, and from 2 to 1-dimensional for infinite length. Temperature predictions were very close to experimental results. Conditions in which elliptical cross section can be approximated by circular cross-section were determined. For this, an equal cross-sectional area, and an equal surface area-to-volume ratio of the elliptical and circular cross sections were considered. The equal circular cross-sectional area approach closely predicted the center temperature only at low ellipse eccentricities (e<0.7). Equal surface area-to-volume ratio approach resulted in good predictions even at high eccentricities (e less than or equal to 0.9).