Transient natural convection in a heat-generating layer of water bounded from below by a segment of a sphere has been experimentally investigated as a model of a possible core-melt configuration. The layer has an insulated lower boundary and a rigid, isothermal upper boundary. These thermal and hydrodynamic boundary conditions have been chosen to provide lower-bound and limiting-case estimates of heat transfer coefficients and temperature profiles within the layer. The data comprise measured maximum temperature differences and temperature profiles within the layer as a function of time. Although the transient temperature profiles exhibit features similar to those of transient convection in a horizontal layer, flow development time-scales are found to be generally greater than for the horizontal layer. A simple relation between the layer Fourier number and Rayleigh number is found to correlate the time-scale data sufficiently well for engineering purposes.