A numerical study of rotating convection driven by horizontal temperature gradients and a radial, spherically symmetric body force in a hemispherical layer is presented. The imposed temperature gradients would result in static stability in the absence of thermal advection (i.e., the inner sphere is cooler than the outer one). The numerical technique calculates the axisymmetric solution to the finite-differenced Navier-Stokes equations, then determines the linear stability of that solution to three-dimensional perturbations. The primary result is the determination of a marginal stability curve in Taylor number (Ta), thermal Rossby number (Rot) parameter space, separating stable axisymmetric flow from nonaxisymmetric flow. Additionally, the structures and energetics of the fastest-growing eigenmodes are examined. This analysis indicates that baroclinic instability of the Eady type is responsible for the instability for much of parameter space, although the modes take on some characteristics of Rayleigh—Bénard (vertical) convection for largeRot. When the equator is warmer than the pole, an unstable centrifugal mode occurs for smallRotand largeTa. The transitions between types of modes are not abrupt, and modes of mixed character are seen in the transition regions.