An aircraft fuel tank pressurization system comprising: at least one on-board fuel tank for storage of aircraft fuel under an internal tank pressure and at an internal ambient tank temperature, the fuel tank having a tank inlet for receiving pressurization air, a tank outlet for discharging fuel from the tank and a tank vent line; a passive heat exchanger having an exchanger inlet (12a-1) configured to be fluid-connected to a propulsion engine (Ep, Es) of the aircraft to receive heated pressurized bleed air therefrom, and an exchanger outlet (12a-2) fluid connected to the fuel tank, the passive heat exchanger being configured to cool the heated pressurized bleed air from the engine (Ep, Es) by heat transfer to an ambient environment by radiation and convection so as to supply pressurization air to the fuel tank at the internal tank pressure and the internal ambient tank temperature; inlet and outlet fixed calibrated orifices (18a, 18b) positioned in the inlet (12a-1) and the outlet (12a-2) of the passive heat exchanger for controllably limiting flow of the bleed air from the engine (Ep, Es) to the heat exchanger and to the fuel tank, respectively, a pressure regulating/shutoff valve (PRSOV) positioned in the inlet of the heat exchanger downstream of the inlet orifice and having opened and closed conditions to respectively fully supply and fully stop flow of the pressurized bleed air to the heat exchanger; and a system controller operatively connected to the PRSOV for modulating the PRSOV between open and closed conditions to maintain pressure and temperature conditions of the pressurization air supplied to the tank by the heat exchanger within predetermined pressure and temperature set point conditions. at least one on-board fuel tank for storage of aircraft fuel under an internal tank pressure and at an internal ambient tank temperature, the fuel tank having a tank inlet for receiving pressurization air, a tank outlet for discharging fuel from the tank and a tank vent line; a passive heat exchanger having an exchanger inlet (12a-1) configured to be fluid-connected to a propulsion engine (Ep, Es) of the aircraft to receive heated pressurized bleed air therefrom, and an exchanger outlet (12a-2) fluid connected to the fuel tank, the passive heat exchanger being configured to cool the heated pressurized bleed air from the engine (Ep, Es) by heat transfer to an ambient environment by radiation and convection so as to supply pressurization air to the fuel tank at the internal tank pressure and the internal ambient tank temperature; inlet and outlet fixed calibrated orifices (18a, 18b) positioned in the inlet (12a-1) and the outlet (12a-2) of the passive heat exchanger for controllably limiting flow of the bleed air from the engine (Ep, Es) to the heat exchanger and to the fuel tank, respectively, a pressure regulating/shutoff valve (PRSOV) positioned in the inlet of the heat exchanger downstream of the inlet orifice and having opened and closed conditions to respectively fully supply and fully stop flow of the pressurized bleed air to the heat exchanger; and a system controller operatively connected to the PRSOV for modulating the PRSOV between open and closed conditions to maintain pressure and temperature conditions of the pressurization air supplied to the tank by the heat exchanger within predetermined pressure and temperature set point conditions.