In cruise ship applications several waste heat recovery systems have been developed over the years in order to harvest the excess heat produced by the diesel engine and is stored in the coolant as thermal energy for instance. In this paper, a detailed model of a Fresh-Water-Cooling system is developed based on first principles and a given circuit scheme provided by the vessel manufacturer. The Fresh-Water Cooling system consists of multiple interconnected subsystems; in this paper the main focus lies on the heat exchanger, where the waste heat recovery process takes place. Due to the presence of unmeasured states and uncertain model parameters the heat exchanger is modelled as partially measured stochastic system. Further the process is proved to be conditionally Gaussian, which makes the use of a conditionally Gaussian filter possible. It produces optimal estimates for the states and the unknown drifting parameters in the mean square sense: The process state is locally stabilized by the estimated process values using stabilizing feedback control. (C) 2016 Elsevier Ltd. All rights reserved.