It is well known that the violence of slow cook-off explosions can greatly exceed the comparatively mild case burst events typically observed for rapid heating. However, there have been few studies that examine the reaction violence as a function of applied heat flux that explore the dependence on heating geometry and device size. Here we report progress on a study using the Uintah Computation Framework, a high-performance computer model capable of modeling deflagration, material damage, deflagration to detonation transition and detonation for PBX9501 and similar explosives. Our results suggests the existence of a sharp threshold for increased reaction violence with decreasing heat flux. The critical heat flux was seen to increase with increasing device size and decrease with the heating of multiple surfaces, suggesting that the temperature gradient in the heated energetic material plays an important role the violence of reactions.