The thermal convection of a fluid with a Rayleigh number of zero, induced by internal heat generation in a bounded cylinder, is studied numerically. The appearance of the convection can be forecast by the analysis of the heat transfer and the stability of the conductive regime between two plates. The numerically determined critical modified Rayleigh number for a large aspect ratio is in good agreement with the linear stability analysis of the infinite fluid layer. The perturbation introduced by a small inclination of the cylinder for the numerical instability study leads to the same results as that of an imposed perturbation velocity in the linear case. The stabilisation due to the confinement appears strongly for an aspect ratio of less than 0.5.