Thermal stability and protection in the event of quench are key issues in the design of superconducting magnets. Quench development and propagation strongly depend on the conductor characteristics and the magnet configuration. An adequate quench protection method must maintain both the peak temperature and the peak voltage during the event within acceptable limits. This paper presents quench modeling and evaluation of candidate protection schemes for a superconducting coil based on a magnesium diboride (MgB2) wire, designed for use in a new cryogen-free magnetic resonance imaging scanner. The wire properties are different, and the current density is significantly higher from those previously reported. In contrast to previous studies, it is concluded that the coil cannot be considered self-protecting and that protection using external resistance provides a practically acceptable solution.