If you want something to absorb heat to a certain point, and then release it when the space around it reduces in temp (Again, 2LoT), what you're describing is a thermal capacitor. From an intellectual standpoint, I ask if that's really a good idea though, and perhaps this isn't the best place to have that conversation.
Still, my thoughts in brief are that in a system with energy both entering and exiting at a constant rate (in from the vents, out through the exhaust), and no external factors, the best way to maintain constant temperature would be (I would think) to isolate that system through insulation so that external forces cannot interfere. I see no bennefit to be gained from a thermal capacitor. Only detriment from having to produce enough heat for it to store. Keep in mind that true insulators do not absorb energy, but rather deflect it.
Thinking about a cooker, when you open and close the door, you let a large amount of heat out, and the thermal capacitor is able to release the heat it has into the space with less temperature (2Lot), requiring less time or fire from the coals to return to temp. Still, with reactionary systems controlling modern cookers (read Stokers and Gurus), they will adjust the amount of heat produced to accomodate the loss of heat from opening the door, and then reduce it later.
So, if you're going to be opening the door to your cooker frequently, I can see how sand may help you stabilize temps, but at a cost of increased fuel consumption to add energy to the heat capacitor. If you have a ADC device on your cooker, I would think you would be better off using insulation than sand, but that's just my geeky opinion as some one who doesn't own one. The other qustion to ask is whether or not sand is the best substance to use as a thermal capacitor. As I said, it has some resistance to thermal conduction, and if your goal is thermal capacitance, I would think you would want something that accepts and receives heat freely, like aluminum. If the goal is to be a thermal barrior (Insulator), I would just think something else would be better.
Just thoughts, sorry for the distraction...
dmp