In this paper, the sensitivity of the efficiency of a fixed cross-sectional fin with temperature-dependent thermal conductivity to various parameters is investigated using the adjoint equation. A one-dimensional steady-state formulation is assumed for both the governing energy equation and the corresponding adjoint equation. The appropriate boundary condition for a convective fin tip is derived for the adjoint variable. The energy and adjoint equations are solved numerically using a finite-difference scheme. The results indicate that a slight increase in certain parameters, such as the cross-sectional area and the base thermal conductivity, leads to an improvement in fin efficiency. In contrast, increasing parameters such as the fluid heat transfer coefficient and the fin length results in a reduction in efficiency. The slope factor in the linear thermal conductivity model exhibits a non-monotonic effect: for negative values, increasing the slope reduces fin efficiency, whereas for positive values, it enhances the efficiency. Furthermore, the Biot number defined along the fin length shows a pronounced negative influence on fin efficiency as it increases. Its most significant impact occurs around a Biot number of 0.1, corresponding to the transition from a nearly uniform temperature distribution to a regime with a pronounced internal temperature gradient.