  We discuss the tempering Monte Carlo method, and its critical slowing down in
the $3d$ Ising model. We show that at $T_c$ the tempering does not change the
critical slowing down exponent $z$. We also discuss the exponential slowing
down for the transition from the plus to the minus state in the cold phase, and
we show that tempering reduces it to a power law slowing down. We discuss the
relation of the flip-flop rate to the surface tension for the local dynamical
schemes.
