This article studies the thermal performance of a moving fin with temperature-dependent thermal conductivity in a convective and radiative environment. It corresponds to a nonlinear heat transfer problem related to the nonlinear ordinary differential equation (NODE) for the unknown temperature excess. The NODE is solved by converting it to a nonlinear Fredholm integral equation. An approximate temperature distribution is determined in the quadratic form for arbitrary values of the Biot and Peclet numbers. A comparison of our results with the previous ones indicates satisfactory accuracy of the obtained solution. The fin efficiency is also given explicitly in terms of prescribed parameters and calculated numerically. The heat dissipation to the surrounding medium due to convection and radiation is analyzed for various speeds of a moving fin. The influences of thermal conductivity, heat convection, radiation, and moving speed of the fin on the temperature distribution and thermal performance are elucidated.