A series of experiments has been undertaken to investigate the onset of convection in a rapidly rotating fluid filled sphere. The boundary is subjected to a time varying temperature allowing the simulation of radial temperature profiles associated with internal heating. The system is similar to that treated theoretically by Roberts (1968), Busse (1970) and Soward (1977). It is found that Busse's modification of Roberts' linear analysis, taking into account velocity perturbations which are antisymmetric about the equatorial plane, provides a good estimate of the temperature gradient required to initiate convection. As observed in the experiments of Carrigan and Busse (1983) and predicted by linear theory, convection appears in the form of rolls or columns, aligned parallel to the rotation axis. As in earlier experiments, observed azimuthal wavenumbers are consistently smaller than predicted which we postulate to be a consequence of nonlinear effects. Owing to the presence of a centrifugally driven thermal wind, the predicted azimuthal drift of the rolls has not been observed.