We consider an incompressible elastic solid which admits a configuration of equilibrium having the shape of a rectangular parallelepiped $C^{*}$ when external forces are absent. We look for a thermoelastic transformation mapping that configuration onto a cylindrical wedge $C$. The problem we consider is analogous to the one where both $C^{*}$ and $C$ are cylindrical crowns. This case has been considered by T. Manacorda$^{(1)}$ Referring $C$ to a system of cylindrical coordinates $r$, $\vartheta$ and $\zeta$, we show that the transformation we look for is compatible in general with a temperature field, $T$, depending upon $r$ only. On the contrary, a field $T$ depending upon $\vartheta$ only or upon $\zeta$ only, does not solve our problem unless the constitutive equations of the body satisfy certain conditions that we write explicitly.