A method of operating a fuel delivery system for an internal combustion engine is described. The system may include a plurality of direct cylinder injectors, a fuel rail upstream of the injectors, a first pump, and a second pump coupled downstream of the first pump and to the fuel rail. The method may include, after or during engine shutdown, and during a fuel system cool down, activating the first pump; and varying the activation of the first pump responsive to temperature to maintain a higher pressure for high temperatures. Alternatively, in some examples, the system may include a reservoir in a bypass around the second pump, the bypass having a valve downstream of the fuel reservoir, where the valve is positioned vertically above the second pump and the fuel reservoir is positioned vertically above the valve. The fuel reservoir may be sized to hold a sufficient amount of fuel in the bypass to allow fuel to migrate from the bypass to the fuel rail during engine cool down.