  We study the formation of domains in a continuous phase transition with a
finite-temperature quench. The model treated is the $\Phi^4$ theory in two
spatial dimensions with global O(2) symmetry. We investigate this using
real-time thermal field theory, following Boyanovsky and collaborators, and
find that domain sizes appear to be smaller than those produced in an
instantaneous quench in the tree-level approximation. We also propose that a
more physical picture emerges by examining the two-point functions which do not
involve any cutoff on the short wavelength Goldstone modes.
