  We study conformal blocks for thermal one-point-functions on the sphere in
conformal field theories of general dimension. These thermal conformal blocks
satisfy second order Casimir differential equations and have integral
representations related to AdS Witten diagrams. We give an analytic formula for
the scalar conformal block in terms of generalized hypergeometric functions. As
an application, we deduce an asymptotic formula for the three-point coeffcients
of primary operators in the limit where two of the operators are heavy.
