) A method to control a fuel pump for a direct injection system provided with a common rail comprising the steps of: calculating the objective fuel flow rate (M ref ) to be fed by the high pressure pump to the common rail instant by instant to have the desired pressure value inside the common rail ; comparing the objective fuel flow rate (M ref ) with the maximum flow rate (M max ) that can be delivered by the high pressure pump wherein in case the difference between objective fuel flow rate (M ref ) and the maximum flow rate (M max ) is irrelevant or lower than a threshold value (TV) that can be adjusted during a set up phase of a control unit , no strategy is implemented in order to control the high pressure pump so as to contain the temperature variation (ΔT) generated during the pumping phase in the high pressure pump ; and in case the difference between the objective fuel flow rate (M ref ) and the maximum flow rate (M max ) that can be delivered by the high pressure pump is not irrelevant and exceeds and adjustable threshold value (TV) a strategy is implemented, which is aimed at containing the temperature variation (ΔT) generated during the pumping phase in the high pressure pump ; and said strategy comprises controlling the high pressure pump so as to alternate exclusively operating cycles of the high pressure pump with the maximum flow rate (M max ) that can be delivered and idle operating cycles of the high pressure pump and in case the objective fuel flow rate (M ref ) is equal to 1/n of the maximum flow rate (M max ) that can be delivered by the high pressure pump , the method comprises the further step of controlling an operating cycle of the high pressure pump with the maximum flow rate (M max ) that can be delivered and (n - 1) idle operating cycles of the high pressure pump . calculating the objective fuel flow rate (M ref ) to be fed by the high pressure pump to the common rail instant by instant to have the desired pressure value inside the common rail ; comparing the objective fuel flow rate (M ref ) with the maximum flow rate (M max ) that can be delivered by the high pressure pump wherein in case the difference between objective fuel flow rate (M ref ) and the maximum flow rate (M max ) is irrelevant or lower than a threshold value (TV) that can be adjusted during a set up phase of a control unit , no strategy is implemented in order to control the high pressure pump so as to contain the temperature variation (ΔT) generated during the pumping phase in the high pressure pump ; and in case the difference between the objective fuel flow rate (M ref ) and the maximum flow rate (M max ) that can be delivered by the high pressure pump is not irrelevant and exceeds and adjustable threshold value (TV) a strategy is implemented, which is aimed at containing the temperature variation (ΔT) generated during the pumping phase in the high pressure pump ; and said strategy comprises controlling the high pressure pump so as to alternate exclusively operating cycles of the high pressure pump with the maximum flow rate (M max ) that can be delivered and idle operating cycles of the high pressure pump and in case the objective fuel flow rate (M ref ) is equal to 1/n of the maximum flow rate (M max ) that can be delivered by the high pressure pump , the method comprises the further step of controlling an operating cycle of the high pressure pump with the maximum flow rate (M max ) that can be delivered and (n - 1) idle operating cycles of the high pressure pump . <EOS>