  We study conformal Ward-Takahashi identities for two-point functions in
$d(\geq3)$-dimensional finite-temperature conformal field theory. We first show
that the conformal Ward-Takahashi identities can be translated into the
intertwining relations of conformal algebra $\mathfrak{so}(2,d)$. We then show
that, at finite temperature, the intertwining relations can be translated into
the recurrence relations for two-point functions in complex momentum space. By
solving these recurrence relations, we find the momentum-space two-point
functions that satisfy the Kubo-Martin-Schwinger thermal equilibrium condition.
