Conventional MRI machines use superconducting magnets with niobium titanium (NbTi), requiring thousands of liters of liquid helium to bathe the superconducting coils. Since helium is a costly nonrenewable resource and in short supply, it would be desirable to have a conduction-cooled superconducting magnet that avoids the use of a liquid helium bath. One such candidate for a conduction-cooled magnet would use magnesium diboride (MgB₂) superconducting wire. Compared to NbTi, which has a critical temperature of 10 K, MgB₂ has a critical temperature of 39 K. Although it is much more difficult to initiate a quench in an MgB₂ magnet compared to an NbTi magnet, it is also much more difficult to protect such a magnet if an unintended quench does occur [1,2]. A passive quench protection system works well for NbTi magnets whereas protection for an MgB₂ magnet would require an active system. Here an active protection system is proposed for a persistent mode 1.5 T MgB₂ magnet [2,3], and a numerical simulation for the full 10 coil magnet is performed. If no protection system were present, a localized hot spot would rapidly grow and damage the coil. By placing heaters on the surfaces of all the coils, the heaters can be activated when a localized hot spot is detected, thereby causing all the coils to rapidly quench. This increases the resistance of the coils, thereby decreasing the current before the hot spot causes damage. These same heaters can be activated in an emergency to quickly bring the field to zero.The heat equation is discretized in space and then integrated in time using a 4th order Runge-Kutta scheme (ODE45) in Matlab. Heaters are placed on the surfaces of all the coils. A hot spot is initiated by letting a section of wire on the surface of coil 1 become resistive. When the voltage across coil 1 becomes greater than 100 mV [4], the heaters are initiated. The total amount of energy input into the outer layer of the coils is 34.4 kJ in 0.2 s, where the amount of energy input into each coil is proportional to the outer surface area of that coil. The wire used for the simulations is based on one from Hyper Tech Research, Inc [5]. In order to bring down the maximum temperature so that the coil is not damaged, variations of this wire are used in the simulations, which include adding more copper, using Glidcop Al-60 [6] instead of Monel, and increasing the thermal conductivity of the wire insulation. Figure 1a shows a plot of the maximum temperature reached on each of the coils for the material percentages shown. Since the hotspot was initiated on the surface of Coil 1, the maximum temperature reached occurs on that coil. The vertical dotted line indicates the time at which the detection voltage reaches 100 mV and the protection heaters are initiated. The maximum temperature is seen to reach almost 300 K which may damage the coil [1]. Increasing the amount of copper to 36% (Fig. 1b) is seen to decrease T_max to about 180 K, which should be safe [1]. If instead of increasing the amount of copper, the Monel sheath is replaced by Glidcop (Fig. 1c), T_max reaches about 150 K, which is even better. Another option is to increase the thermal conductivity of the insulation. By increasing this quantity by a factor of 3 (Fig. 1d), T_max is decreased to about 180 K, which is again safe. A numerical simulation of the heat equation was performed for a persistent mode 1.5 T MgB₂ conduction-cooled magnet. A hot spot was initialized by allowing a section of wire on the surface of Coil 1 to become resistive. An active protection system was employed using surface heaters on all the coils, which were initiated when the voltage across Coil 1 became greater than 100 mV. Using the standard wire (15% Cu, 15% SC, 45% Monel), the temperature was found to reach nearly 300 K, which may damage the coil. By increasing the amount of copper, using Glidcop instead of Monel, or increasing the thermal conductivity of the insulation by a factor of 3, the temperature is kept within safe limits, the use of Glidcop giving the best performance.