Small air intakes, on the warming box near the bottom, on each side, should get you a cooler warming box.... adjustable and even heat....
Do you have an upper air inlet on the firebox?? You might try that also.... It helps to move the air from the firebox to the cook chamber.... At times, the FB gets really hot... cutting down on the air below the fire, to cool it, also cuts down on the air through the CC.... With the upper air inlet, moving the heat/air through the CC seems a better choice to control the temps.... The whole heat thing is a balancing act using air movement for a control....
Dave