Heat flows into a cooling fin conductively from its base (root) and dissipates convectively into ambient fluid along its surface. The temperature difference between the fin and ambient fluid $(T - T_\infty)$ is highest at the root and lowest at the tip. Therefore, convective heat dissipation per unit area ($q = h A \Delta T$) is greatest near the root. Designing the fin with maximum surface area/thickness at the root (such as in triangular or parabolic fins) maximizes heat dissipation efficiency.