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Abstract This paper investigates a radially symmetric inverse heat conduction problem, which determines the internal surface temperature distribution of the hollow sphere from measured data at the fixed location inside it. This is an inverse and ill-posed problem. A conditional stability estimate is given on its solution by using Hölder’s inequality. A wavelet regularization method is proposed to recover the stability of solution, and the technique is based on the dual least squares method and Shannon wavelet. A quite sharp error estimate between the approximate solution and the exact ones is obtained by choosing a suitable regularization parameter.