  We consider finite temperature properties of the Ising chain in a transverse
field in the vicinity of its zero temperature, second order quantum phase
transition. New universal crossover functions for static and dynamic
correlators of the ``spin'' operator are obtained. The static results follow
from an early lattice computation of McCoy, and a method of analytic
continuation in the space of coupling constants. The dynamic results are in the
``renormalized classical'' region and follow from a proposed mapping of the
quantum dynamics to the Glauber dynamics of a classical Ising chain.
