  We provide an exact finite temperature extension to the recently developed
Riemann-Hilbert approach for the calculation of response functions in
nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise
definition of the finite temperature Riemann-Hilbert problem and show that it
is equivalent to a zero temperature problem. Using this equivalence, we discuss
the solution of the nonequilibrium Fermi-edge singularity problem at finite
temperatures.
