The onset of convection in a narrow cylindrical annulus heated from below and rotating about its vertical axis of symmetry is considered in the case when the rigid cylindrical walls are thermally insulating. An analytical expression is derived for the Rayleigh number $R$ for onset of convection as a function of rotation rate and azimuthal wavenumber. The critical value $R_c$ for high rotation rates is much lower than the corresponding value in an extended layer. At finite amplitudes the convection flow generates a differential rotation which is antisymmetric with respect to the middle of the layer and is prograde near the outer wall for low rotation rates, but changes sign for higher values of the rotation parameter.