  In this work we study the time evolutions of (Renyi) entanglement entropy of
locally excited states in two dimensional conformal field theories (CFTs) at
finite temperature. We consider excited states created by acting with local
operators on thermal states and give both field theoretic and holographic
calculations. In free field CFTs, we find that the growth of Renyi entanglement
entropy at finite temperature is reduced compared to the zero temperature
result by a small quantity proportional to the width of the localized
excitations. On the other hand, in finite temperature CFTs with classical
gravity duals, we find that the entanglement entropy approaches a
characteristic value at late time. This behaviour does not occur at zero
temperature. We also study the mutual information between the two CFTs in the
thermofield double (TFD) formulation and give physical interpretations of our
results.
