This paper addresses the problem of adaptive fitting of a stochastic model to what is known as Human Body Daily Temperature Dynamics (HBDTD). HBDTD belongs to the class of systems whose state processes are unobtainable for any practical use and can therefore be regarded as hidden signals. Hence, the only criterion for stochastic model fitting appears to be the output (measured) process used in Minimum Prediction Error (MPE) identification methods. Recently however, a relatively novel methodology known as the Active Principle of Adaptation (APA) was developed and generalized for the purpose of time-variant system identification. In contrast to MPE methods, the APA-based approach considers Exact System Models rather than Approximate System Models and hence yields a new Minimum State Prediction Error method. The solution outlined in this paper is based on replacing the direct model fitting by the indirect one and employing HBDTD adaptive stochastic modeling to demonstrate how modern, i.e. numerically stable MSPE computations can be successfully put to practical use in today's health care.