Continuous, mathematically smooth Phase Objects with radial symmetry are reconstructed from cross sections of their refractive index distribution by a novel method, consisting of a linear combination of Gaussian basis functions, whose technical details are discussed. As an application example, this approach is used to get a fast and accurate estimation of the temperature distribution of an actual soldering tip. [DOI: http://dx.doi.org/10.2971/jeos.2013.13036]