One-point thermal conformal blocks from four-point conformal integrals

We develop the thermal shadow formalism to study the conformal blocks decomposition in D-dimensional conformal field theory on Sβ¹ × SD-1, where the temperature is T = β⁻¹. It is demonstrated that both the 1-point thermal (T≠ 0) conformal blocks and the 4-point plane ($T=0$) conformal blocks are defined by the same 4-point conformal integral. It is shown that up to power prefactors the 1-point thermal conformal block is given by the fourth Appell function.