  We develop the thermal shadow formalism to study the conformal blocks
decomposition in $D$-dimensional conformal field theory on
$\mathbb{S}_{\beta}^{1} \times \mathbb{S}^{D-1}$, where the temperature is $T =
\beta^{-1}$. It is demonstrated that both the 1-point thermal ($T\neq 0$)
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.
