Owing that the modified straight fin with round base and round tip possesses a pronounced irregular profile area, the one-dimensional modeling with the simplistic quasi one-dimensional heat conduction equation is inappropriate. Switching to the two-dimensional modeling, the governing two-dimensional heat conduction equation in Cartesian coordinates cannot be solved analytically and forcibly has to be done numerically with the potent finite element method. The two-dimensional temperature distributions and the companion heat transfer rates are computed for the two distinct straight fins with rectangular profile using realistic combinations of the transverse Biot number and the aspect ratio normally used in engineering practice. At the end, the maximum heat transfer enhancement granted by the modified straight fin with round base and round tip having small-to moderate aspect ratios can reach a favorable 12% margin.