A system and a method are for heat treatment of water of a vessel outside a fixed installation of the vessel. The water includes ballast water of the vessel and/or waste water from hull cleaning of the vessel. The system includes a system inlet; a system outlet; a heat application section; and a heat treatment piping system. A heat recovering section includes two parts for exchanging heat. The heat treatment piping system couples the system inlet to the system outlet via: one of the parts of the heat recovering section, the heat application section and the other part of the heat recovering section. The system does not form part of a fixed installation of the vessel.