  Dwell time for a two state particle tunneling through a noisy thermal
magnetic barrier has been calculated by studying the time evolution of the
system. The effect of temperature has been included by averaging over the
environmental magnetic modes. The time scale has been calculated in the
framework of weak measurement. The dwell time initially increases with the rise
of temperature and finally saturates. The increment of dwell time can be
explained by the phenomena of quantum memory loss caused by efficient energy
exchange with the environmental modes. The saturation region at higher
temperature corresponds to the process of thermal hopping of the barrier.
