I realize there haven't been any posts on this topic for a while, but it is an important subject. My company has plenty of experience with supplying solid exotic woods for radiant heat. We commonly recommend 2-1/4" and 3" in Jatoba / Brazilian Cherry, Ipe, and TigerWood.
Sometimes, it is possible to find solid wood material that is selected for grain orientation. Solid wood generally expands and contracts by a factor of 2:1, comparing tangential to radial grain orientation. Imagine looking at the end of the log and seeing the concentric growth rings. Tangential is along the growth rings and radial is from the very center of the tree to the outside.
Because solid wood will expand twice as much tangentially, if you can orient all the growth ring vertically, the material will be more stable in width - and that's what you want when dealing with radiant heat. The industry terms for this type of grain selection is quarter sawn, straight grain or vertical grain.
There are some resources on the web that list the tangential and radial expansion percentages for many species. You can check out my site at www.novausawood.com
for more info.
I hope you find this information helpful. Steve