  We study 2-point and 3-point functions in CFT at finite temperature for large
dimension operators using holography. The 2-point function leads to a universal
formula for the holographic free energy in $d$ dimensions in terms of the
$c$-anomaly coefficient. By including $\alpha'$ corrections to the black brane
background, one can reproduce the leading correction at strong coupling. In
turn, 3-point functions have a very intricate structure, exhibiting a number of
interesting properties. In simple cases, we find an analytic formula, which
reduces to the expected expressions in different limits. When the dimensions
satisfy $\Delta_i= \Delta_j+ \Delta_k$, the thermal 3-point function satisfies
a factorization property. We argue that in $d>2$ factorization is a reflection
of the semiclassical regime.
