  We consider weakly-coupled QFT in AdS at finite temperature. We compute the
holographic thermal two-point function of scalar operators in the boundary
theory. We present analytic expressions for leading corrections due to local
quartic interactions in the bulk, with an arbitrary number of derivatives and
for any number of spacetime dimensions. The solutions are fixed by judiciously
picking an ansatz and imposing consistency conditions. The conditions include
analyticity properties, consistency with the operator product expansion, and
the Kubo-Martin-Schwinger condition. For the case without any derivatives we
show agreement with an explicit diagrammatic computation. The structure of the
answer is suggestive of a thermal Mellin amplitude. Additionally, we derive a
simple dispersion relation for thermal two-point functions which reconstructs
the function from its discontinuity.
