We study the nematic-smectic phase transition of a thermotropic liquid crystal confined to a spherical shell. Far from the nematic-smectic phase transition temperature, T(NS), we observe a configuration with four +1/2 defects, as predicted by theory. Since in this case K(1)≈K(3), the four defects are confined at the thinnest part of the shell to minimize the energy associated with the defect cores. By contrast, near T(NS), where K(3)≫K(1), bend distortions become prohibited and the defects organize themselves along a great circle of the sphere, confirming recent theoretical and simulation results. During this structural change, the defects associate in two pairs that behave independently. In the smectic phase, we observe a new configuration displaying curvature walls.