The inverse heat conduction problem, IHCP, refers to the type of heat conduction problems, in which part or all of the thermal boundary conditions imposed on the body are unknown; instead, measured temperature data at certain locations within the body interior or at its surface are available. The task is, usually an estimation of the unknown boundary condition, which, in a great majority of the cases, is the surface heat flux. The problem is mathematically ill-posed, meaning that a small error in the measured data (due to inevitable noise in the data) greatly contaminates estimation of the boundary condition.This paper discusses a non-classical method for the solution of the IHCP, namely Artificial Neural Networks. In this method, first, the neural network is "trained" how to estimate the heat flux in a particular system by using a set of known heat flux components, as well as a set of "measured" data, both of which can either be obtained by actual experiments performed on the system or, equally as well, by performing simulated experiments, using a "direct" heat conduction solution. Once the training (i.e. system identification) is complete, the neural network algorithm can be used for estimation of any unknown surface heat flux history for that particular system. The neural network algorithm used in this work consists of a 3-layer perceptron, a training algorithm of resilient error back propagation, which is quite improved, as compared to the one used previously by Raudensky et al for simultaneous parameter and function estimations. It is shown, via a classical triangular heat flux test case, that the method can yield accurate, as well as stable, estimations. The method does not require calculation of the sensitivity coefficients and it is shown that the well-known lagging and damping effects in classical IHCP is not a particularly important issue for this algorithm, as the estimation of heat flux by sensors located far from the active surface are almost equally as good as those located near it.