The presence of thermal diffusivity in a spherical thermal anemometer gives it long-memory dependence. The identification problem and state realisation of this model is addressed by using diffusive representation (DR). In order to do that, an ideal thermal sphere quadrupole model and its corresponding finite differences model are proposed and simulated. From those models and the non-rational Cole-Cole transfer function, the identification problem is discussed. PRBS as an input signal is also discussed. The best choice in the number of poles and their position is found by analysing frequency response. For the 5 decades bandwidth used here, it has been found that 8 poles geometrically spaced by a scale factor of 5 is a good choice. Finally, 8 poles DR is verified as a good option to model a complex spherical thermal anemometer prototype which is being developed in Universitat Politècnica de Catalunya, by means of open loop and sigma-delta closed loop control simulations.