Coinjection molding shooting pot cooling apparatus and method are configured to cool a shooting pot cylinder which, in combination with a shooting pot piston, injects a melt through a coinjection nozzle having at least two melt channels ending at the same gate. Preferably, a heat sink sleeve is disposed to contact an outer surface of a rear portion of the shooting pot cylinder. The heat sink sleeve is configured to remove sufficient heat from the shooting pot cylinder to increase the viscosity of the melt therein, thus reducing melt leakage between the shooting pot piston and the shooting pot cylinder.