  In strongly coupled conformal field theories with a large central charge
important light degrees of freedom are the stress tensor and its composites,
multi-stress tensors. We consider the OPE expansion of two-point functions of
the stress tensor in thermal and heavy states and focus on the contributions
from the stress tensor and double-stress tensors in four spacetime dimensions.
We compare the results to the holographic finite temperature two-point
functions and read off conformal data beyond the leading order in the large
central charge expansion. In particular, we compute corrections to the OPE
coefficients which determine the near-lightcone behavior of the correlators. We
also compute the anomalous dimensions of the double-stress tensor operators.
