A mathematical model is developed and used for a computer simulation of the thermoregulation of premature infants. We propose a finite volume technique for the solution of the associated partial differential equation on an unstructured grid. Emphasis is laid on the model and the validation of the numerical scheme. Beside various test runs using real life data, we present a discrete maximum principle for the steady state solution with respect to the non‐convex computational domain. Keywords: Finite volume method, Thermoregulation, Maximum principle.