A system for cooling an aircraft fuel cell system comprising a first cooling circuit thermally coupled to a first fuel cell, to remove thermal energy generated by the first fuel cell during operation from the first fuel cell, and a first heat exchanger arranged in the first cooling circuit and adapted to transfer thermal energy, removed from the first fuel cell via the first cooling circuit, to the aircraft surroundings. The system comprises a second cooling circuit thermally coupled to a second fuel cell, to remove thermal energy generated by the second fuel cell during operation from the second fuel cell, and a second heat exchanger arranged in the second cooling circuit and adapted to transfer thermal energy, removed from the second fuel cell via the second cooling circuit, to the aircraft surroundings. The first cooling circuit is thermally couplable to the second cooling circuit.