Allostasis proposes that long-term viability of a living system is achieved through anticipatory adjustments of its physiology and behaviour: emphasising physiological and affective stress as an adaptive state of adaptation that minimizes long-term prediction errors. More recently, the active inference framework (AIF) has also sought to explain action and long-term adaptation through the minimization of future errors (free energy), through the learning of statistical contingencies of the world, offering a formalism for allostatic regulation. We suggest that framing prediction errors through the lens of biological hormonal dynamics proposed by allostasis offers a way to integrate these two models together in a biologically-plausible manner. In this paper, we describe our initial work in developing a model that grounds prediction errors (surprisal) into the secretion of a physiological stress hormone (cortisol) acting as an adaptive, allostatic mediator on a homeostatically-controlled physiology. We evaluate this using a computational model in simulations using an active inference agent endowed with an artificial physiology, regulated through homeostatic and allostatic control in a stochastic environment. Our results find that allostatic functions of cortisol (stress), secreted as a function of prediction errors, provide adaptive advantages to the agent's long-term physiological regulation. We argue that the coupling of information-theoretic prediction errors to low-level, biological hormonal dynamics of stress can provide a computationally efficient model to long-term regulation for embodied intelligent systems.