Developing mathematical models describing pipe (or duct) temperature is of great importance, since pipes are unavoidable elements in most (hydraulic) heating systems, in which some heat transfer fluid flows/circulates between neighbouring working components (such systems are district, central or solar heating systems, etc.). In the present study, the Newton's law of cooling is completed with a recent explicit equation determining the time delay of pipes. Based on measured data, the gained mathematical model, called physically-based model, describes the outlet (fluid) temperature of pipes with a convenient accuracy with respect to the practice. A further model, called LR model, is worked out based on multiple linear regression. Based on measured data, the LR model can model the outlet temperature of pipes generally more precisely than the physically-based model if the flow rate is nonzero. In addition, the LR model has lower computational demand. Since the physically-based model is still more precise under certain conditions, a third model, called grey-box model, is proposed as a combination of the physically-based and the LR model calculating every time according to the more advantageous one of them. Based on measured data, the grey-box model is the most precise model. In addition, this model has lower computational demand than the physically based model. (C) 2016 Elsevier Ltd. All rights reserved.