The main object of this paper is to Introduce the Pseudo Analytic Finite Partition method and to illustrate its use in solving physiological heat distribution problems pertaining to limbs and similar body organs. A two dimensional circular region resembling the cross section of a human or animal limb is considered. The biological properties are assumed to vary along the radial direction. The theoretical model incorporates the effect of blood mass flow and metabolic heat generation. The region is divided into annular sub-regions and Ritz variational finite element method is applied along the radial direction, while for the angular direction, Fourier Series has been used due to uniformity in each annular part.