The stability conditions that take into accounts the size of superconducting magnets and the refrigeration capacity of cryocoolers are investigated for the conduction-cooled systems without liquid cryogens. The worst scenario in the superconducting systems is that the heat generation in the resistive state exceeds the refrigeration, causing a rise in the temperature of the magnet winding and leading to burnout. It is shown by an analytical solution that in the continuously resistive state, the temperature may increase indefinitely or a stable steady state may be reached, depending upon the relative size of the magnet with respect to the refrigeration capacity of the cryocooler. The stability criteria include the temperature-dependent properties of the magnet materials and the refrigeration characteristics of the cryocooler. A useful graphical scheme is presented and the design of the stable magnet/cryocooler interface is demonstrated.