  In d-dimensional CFTs with a large number of degrees of freedom an important
set of operators consists of the stress tensor and its products, multi stress
tensors. Thermalization of such operators, the equality between their
expectation values in heavy states and at finite temperature, is equivalent to
a universal behavior of their OPE coefficients with a pair of identical heavy
operators. We verify this behavior in a number of examples which include
holographic and free CFTs and provide a bootstrap argument for the general
case. In a free CFT we check the thermalization of multi stress tensor
operators directly and also confirm the equality between the contributions of
multi stress tensors to heavy-heavy-light-light correlators and to the
corresponding thermal light-light two-point functions by disentangling the
contributions of other light operators. Unlike multi stress tensors, these
light operators violate the Eigenstate Thermalization Hypothesis and do not
thermalize.
