We leverage the Keldysh formalism to extend our implementation of finite temperature coupled cluster theory [J. Chem. Theory Comput. 2018, 14, 5690-5700] to thermal systems that have been driven out of equilibrium. The resulting Keldysh coupled cluster theory is discussed in detail. We describe the implementation of the equations necessary to perform Keldysh coupled cluster singles and doubles calculations of finite-temperature dynamics, and we apply the method to some simple systems including a Hubbard model with a Peierls phase and an ab initio model of warm-dense silicon subject to an ultrafast XUV pulse.