  We present a numerically exact approach for evaluating vibrationally resolved
electronic spectra at finite temperatures using the coherence thermofield
dynamics. In this method, which avoids implementing an algorithm for solving
the von Neumann equation for coherence, the thermal vibrational ensemble is
first mapped to a pure-state wavepacket in an augmented space, and this
wavepacket is then propagated by solving the standard, zero-temperature
Schr\"odinger equation with the split-operator Fourier method. We show that the
finite-temperature spectra obtained with the coherence thermofield dynamics in
a Morse potential agree exactly with those computed by Boltzmann-averaging the
spectra of individual vibrational levels. Because the split-operator
thermofield dynamics on a full tensor-product grid is restricted to
low-dimensional systems, we briefly discuss how the accessible dimensionality
can be increased by various techniques developed for the zero-temperature
split-operator Fourier method.
