If you light the pit kiln directly by looking at it with a fire starting item (both flint and steel and the firesticks do this) you can light the pit kiln as normal, but if you have, for example, a block of dirt above and diagonal to the pit kiln (as shown in the included screenshots) you can "place" the fire against that block, thereby having fire on top of the pit kiln without the pit kiln actually starting to burn. No timer is shown, and I ran two pit kilns, one lit with each method, and only the one lit by directly "placing" the fire on top of the pit kiln actually did anything. The other fire remained indefinitely without firing the clay molds I placed inside and without burning out. A pit kiln will normally relight itself if extinguished, but a pit kiln "lit" in this way can be extinguished with no reignition and no change to the contents of the kiln.

Side note: in the screenshots I have fired molds in my inventory but this is only from picking up the items from previous tests when trying to recreate another bug I experienced related to pit kilns.