Correct. Possibly much longer. Simply closing vents won't do it. Cutting the draft might curtail or limit the burn, but it will not affect the heat that has been absorbed by the clay. That will be released for some time.
Yes, Dave, I am saying precisely that. If the fire is under control and kept restricted, fine. But if it gets away from you the clay will heat and keep heating as long as the fire is there. Though there will be some delay (and this delay will cause cooker therms, especially at the grate, not to register the problem for a while), rising temps below will cause the clay to absorb increasing heat. Because the clay does not convert the heat to another form (as water does with steam) it does not have the heat sink capabilities of water. It will release the heat as heat - at significantly higher temps. The end of this, then, is also delayed, much like how rocks heated in a campfire, or asphalt in the sun, stay hot much longer after the fire is put out or the sun goes down, which is what Dan is saying.