This paper deals with temperature distribution in a moving fin. Practically, we know that thermal conductivity changes with temperature. So in our study, we consider thermal conductivity as temperature-dependent which is constant, linear, quadratic and exponential. The heat transfer coefficient is taken as a power-law type form in the present work. Internal heat generation has been taken as temperature-dependent. For solving the problem, we used numerical methods such as Legendre wavelet collocation method (LWCM), least square method (LSM) and moment method (MM). An exact solution is computed in a particular case. The percentage error is calculated to find out the most suitable method for solving the problem, which is given in the tabular form. The effect of differentparameters on temperature distribution is studied in detail. The whole paper is presented in dimensionless form.