We examine the ability of neural networks to estimate the tissue perfusion values present and the minimum temperature in numerically calculated (Pennes, Bioheat Transfer Equation) steady-state hyperthermia temperature fields based on a limited number of measured temperatures within this field A hierarchical system of neural networks consisting of a first layer of pattern recognizing neural networks and a second layer of hypersurface reconstructing neural networks is shown to be capable of estimating these variables within a selected error tolerance. The results indicate that estimating the minimum tumour temperature directly with the system of neural networks may be more effective than using the indirect method of numerically recreating a temperature field with perfusion estimates and then obtaining the minimum tumour temperature from the estimated temperature field. Additional results indicate that if the locations of the measured temperatures within the temperature field are selected appropriately, the hierarchical system of neural networks can tolerate a moderate level of model mismatch. This model mismatch can come from errors in modelling the tumour boundaries, the sensor locations, or the magnitude of the power deposition. This paper is not intended to assess or demonstrate clinical applicability but to be a first step in investigating the feasibility of neural networks for parameter estimation related to hyperthermia studies.