We investigate the influence of thermal boundary conditions imposed on the horizontal walls of a differentially heated cavity on the triggering of unsteady solutions to the 2-D Boussinesq equations. We determine the critical values of the Rayleigh number at which unsteady convection appears in a cavity with perfectly conducting horizontal boundaries of aspect ratio in the range 1 to 10 and compare with those previously obtained in the case of adiabatic horizontal walls. It is shown that for small aspect ratio cavities the new boundary condition can have a dramatic effect on the value of the critical Rayleigh number since the basic mechanism leading to unsteady motion is then associated to a thermal instability of the flow. We furthermore show that this bifurcation possesses all the characteristic features of a Hopf bifurcation and this can be used to determine with accuracy the critical Rayleigh number.