Inverse radiation problems were solved for estimating boundary temperature distribution in a way of function estimation approach in an axisymmetric absorbing, emitting and scattering medium, given the measured radiative data. In order to reduce the computational time fur the calculation of sensitivity matrix, automatic differentiation and Broyden combined method were adopted, and their computational precision and efficiency were compared with the result obtained by finite difference approximation.. In inverse analysis, the effects of the precision of sensitivity matrix, the number of measurement points and measurement error on the estimation accuracy had been inspected using quasi-Newton method as an inverse method. Inverse solutions were validated with the result acquired by additional inverse methods of conjugate-gradient method or Levenberg-Marquardt method.