Combining a lattice path integral formulation for thermodynamics with the
solution of the quantum inverse scattering problem for local spin operators, we
derive a multiple integral representation for the time-dependent longitudinal
correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature
and in an external magnetic field. Our formula reproduces the previous results
in the following three limits: the static, the zero-temperature and the XY
limits.