Thickness of wood I realize can be a factor too.
Especially if the wood is not at the same dryness through out. Maybe the absolute dryness is not as important as the differential dryness in the crossection. A piece of wood that is drying has internal stresses that show up when the wood finally breaks open, or a check pops open. This is also related to how strong the wood is in tension across the grain. As DC points out, some species have less strength that way than others.
As a generality, I would say that the closer the middle of the piece is to the dryness of the surface you are heat treating, the better off you are. especially if the wood is not as dry as you might hope
Does anyone pre-soak with water?
mineral oil usp is unscented, unlike baby oil, and can be found in the laxative section at the drug store