The heat flux incident upon the inner surface of a plasma discharge tube during a helicon plasma discharge was estimated using an inverse method. Temperature readings were taken from the outer surface of the tube using thermocouples, and the temperature data were interpolated over the tube surface. A numerical inverse procedure based on the Alifanov iterative regularisation method was used to reconstruct the heat flux on the tube inner surface as a function of space and time. In contrast to previously-used inverse models for this application, the current model implements a thermal radiation boundary condition to realistically model the energy exchange in the device. Additionally in these experiments, steady-state operation was reached, and the accurate modelling of the steady-state condition was facilitated by the thermal radiation boundary condition. The variation of heat flux with helicon discharge power, propellant flowrate, and electromagnet current was studied, and it was found that the waste heat flux increased with applied RF power and propellant flowrate, and decreased with current supplied to the electromagnets, over the range of parameter variation tested. (C) 2014 Published by Elsevier Ltd.