  For the two dimensional kinetic Ising model at finite temperature, the local
mean magnetisation $M_t=t^{-1}\int_{0}^t\sigma(t')\d t'$, simply related to the
fraction of time spent by a given spin in the positive direction, has a
limiting distribution, singular at $\pm m_0(T)$, the Onsager spontaneous
magnetization. The exponent of this singularity defines the persistence
exponent $\theta$. We also study first passage exponents associated to
persistent large deviations of $M_t$, and their temperature dependence.
