Electricity generation system including: - a first fuel cell having a first operating temperature range; - a first cooling circuit containing a heat-transfer fluid passing through the first fuel cell; - a second fuel cell having a second operating temperature range, the lower boundary of which is higher than the higher boundary of the first operating range; - a second cooling circuit containing a heat-transfer fluid passing through the second fuel cell; characterized in that: - the first cooling circuit includes a branch configured for the heat-transfer fluid that has passed through the first fuel cell to pass therethrough; - the system further comprises a device for heating the heat-transfer fluid present in the branch; - a first valve or combination of valves (301, 302) configured to selectively interrupt or allow a flow of heat-transfer fluid through the branch when the heat-transfer fluid is passing through the first fuel cell; - a second valve or combination of valves configured: - either to selectively interrupt or allow a flow of heat-transfer fluid from the branch to the second fuel cell; - or to selectively interrupt or allow a flow of heat-transfer fluid from the branch through a heat exchanger, the second cooling circuit also passing through the heat exchanger; - a control module configured to simultaneously control: - a reheating of the heat-transfer fluid present in the branch; - a flow of heat-transfer fluid through the second fuel cell; - a flow of heat-transfer fluid from the branch through the second fuel cell or a flow of the heat-transfer fluid from the branch through said exchanger. - a first fuel cell having a first operating temperature range; - a first cooling circuit containing a heat-transfer fluid passing through the first fuel cell; - a second fuel cell having a second operating temperature range, the lower boundary of which is higher than the higher boundary of the first operating range; - a second cooling circuit containing a heat-transfer fluid passing through the second fuel cell; - the first cooling circuit includes a branch configured for the heat-transfer fluid that has passed through the first fuel cell to pass therethrough; - the system further comprises a device for heating the heat-transfer fluid present in the branch; - a first valve or combination of valves (301, 302) configured to selectively interrupt or allow a flow of heat-transfer fluid through the branch when the heat-transfer fluid is passing through the first fuel cell; - a second valve or combination of valves configured: - either to selectively interrupt or allow a flow of heat-transfer fluid from the branch to the second fuel cell; - or to selectively interrupt or allow a flow of heat-transfer fluid from the branch through a heat exchanger, the second cooling circuit also passing through the heat exchanger; - either to selectively interrupt or allow a flow of heat-transfer fluid from the branch to the second fuel cell; - or to selectively interrupt or allow a flow of heat-transfer fluid from the branch through a heat exchanger, the second cooling circuit also passing through the heat exchanger; - a control module configured to simultaneously control: - a reheating of the heat-transfer fluid present in the branch; - a flow of heat-transfer fluid through the second fuel cell; - a flow of heat-transfer fluid from the branch through the second fuel cell or a flow of the heat-transfer fluid from the branch through said exchanger. - a reheating of the heat-transfer fluid present in the branch; - a flow of heat-transfer fluid through the second fuel cell; - a flow of heat-transfer fluid from the branch through the second fuel cell or a flow of the heat-transfer fluid from the branch through said exchanger.