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The thermal management of a Formula 1 car is a challenging task as it involves multiple components, systems and multiple sources of thermal energy. The present work attempts to model a representative F1 car following 2018 F1 regulations directly linked to the cooling systems requirements and performance. The main purpose of this work is to simulate the steady and transient behaviour of the cooling system when the vehicle is in a qualifying lap, and during the entire race, including the wait in the starting grid and the pit stops. This model includes the sub-models representing internal combustion engine, hybrid powertrain, vehicle, driver and an appropriate cooling system composed of radiators, pumps and expansion tanks. This work validates the cooling system of a representative 2018 F1 car for the Silverstone Circuit. This model is capable of simulating the overall thermal performance of the F1 car for sizing the cooling system for most of the F1 circuits.