  It has been shown recently that extreme Reissner-Nordstr\"{o}m black holes
perturbed by a minimally coupled, free, massless scalar field have permanent
scalar hair. The hair - a conserved charge calculated at the black hole's event
horizon - can be measured by a certain expression at future null infinity: the
latter approaches the hair inversely in time. We generalize this newly
discovered hair also for extreme Kerr black holes. We study the behavior of
nearly extreme black hole hair and its measurement at future null infinity as a
transient phenomenon. For nearly extreme black holes the measurement at future
null infinity of the length of the newly grown hair decreases quadratically in
time at intermediate times until its length becomes short and the rate at which
the length shortens further slows down. Eventually, the nearly extreme BH
becomes bald again like non-extreme BHs.
