  We present an exact formula for the thermal scalar two-point function in
four-dimensional holographic conformal field theories. The problem of finding
it reduces to the analysis of the wave equation on the AdS-Schwarzschild
background. The two-point function is computed from the connection coefficients
of the Heun equation, which can be expressed in terms of the
Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory
with four fundamental hypermultiplets. The result is amenable to numerical
evaluation upon truncating the number of instantons in the convergent expansion
of the partition function. We also examine it analytically in various limits.
At large spin the instanton expansion of the thermal two-point function
directly maps to the light-cone bootstrap analysis of the heavy-light
four-point function. Using this connection, we compute the OPE data of
heavy-light double-twist operators. We compare our prediction to the
perturbative results available in the literature and find perfect agreement.
