In this paper, we investigate a spherically 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 problem is ill-posed, and a conditional stability result of its solution is given. A modified quasi-boundary value method is proposed to solve the ill-posed problem. Two Ho¨lder-type error estimates between the approximation solution and its exact solution are obtained under an a priori and an a posteriori regularization parameter selection rule, respectively.