The thermal stability conditions are investigated for superconducting magnet systems cooled conductively by cryocooler without liquid cryogens. The worst scenario in the 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 the burnout. It is shown by an analytical solution that in the continuous 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 discussed to demonstrate the physical importance of the results.