  We present a simple Lie-algebraic approach to momentum-space two-point
functions of two-dimensional conformal field theory at finite temperature dual
to the BTZ black hole. Making use of the real-time prescription of AdS/CFT
correspondence and ladder equations of the Lie algebra $\mathfrak{so}(2,2)
\cong \mathfrak{sl}(2,\mathbb{R})_{L} \oplus \mathfrak{sl}(2,\mathbb{R})_{R}$,
we show that the finite-temperature two-point functions in momentum space
satisfy linear recurrence relations with respect to the left and right momenta.
These recurrence relations are exactly solvable and completely determine the
momentum-dependence of retarded and advanced two-point functions of
finite-temperature conformal field theory.
