The moisture content can make a huge difference in size. I was making round lamps and was calculating the diameter of the top and bottom rings, only to discover that as the wood dried it would be as much as a half-inch shorter in the time it took me to cut and finish the top and bottom leaving such a huge gap that I came up with the handle to fill in that gap. worse different woods do this differently.
Warping as it is heated is a different problem and trying to leave no space between the different parts will leave nothing to keep this from happening, not aligning may leave out huge amounts of waste, but I see two solutions, One is to leave an eighth-inch ish space between the parts, but a much trickier way to go is to break up the design in different colors so no two of the same color touch. That way the cuts will not be able to warp the wood at all as long as it was well pinned down until the last cut and then all the old cuts will have had time to cool off and settle down.