The mollification and wavelet prefiltering methods are employed in the ill-posed inverse heat conduction problem of heat flux estimation in a porous medium. The estimation of transient heat flux using the conjugate gradients method along with the adjoint differential equations has been carried out under a nonthermal equilibrium condition. The temperature sensor is located on the inactive surface of porous medium and the effects of the two already-mentioned prefiltering methods on the estimation of heat flux are studied for different noise levels. By smoothing the temperature data, the degree of difficulty of the estimation is reduced considerably. Comparison of the two filtering methods shows that a comparable improvement in performance can be achieved when using both filtering methods via mitigating the ill-posed nature of the problem. The performance of wavelet filter is somewhat superior to the mollification filter; however, the later can be implemented much more conveniently in a computer program.