I would like to have thermal properties of r-plane.

Usually the different sapphire physical properties are for two orientations: parallel to C- axis and perpendicular to C- axis.

And I would like recommend you to look the book: E.Dobrovinskaya, L.Lytvynov, V.Pischik “Sapphire in Science and Engineering”. Kharkov. 2008. It is enough good handbook. I hope it can help you.