By using theoretical analysis and numerical simulation, the stability and the paramagnetism of Fermi gas in a strong magnetic field at low temperatures are studied, and the influences of temperature and magnetic field on the stability and susceptibility of the system are analyzed. The results show that the strong magnetic field causes variation of a system stability, and such a change relates to temperature. While the effects of temperature on stability and susceptibility are relevant to the chemical potential (i.e. the particle number density) of free gas. When the chemical potential is even, the magnetic field weakens the stability of the system, and the increasing of temperature leads to the reduction in the susceptibility of the system. When the chemical potential is odd, the magnetic field strengthens the stability of the system, while the increasing of temperature can increase the susceptibility of the system. With temperature increasing, the effect of the magnetic field on the stability is weakened. With magnetic field increasing, the change of the stability of the system becomes oscillatory, and the oscillation center of the susceptibility shifts down.