  It has long been known that two-point functions of conformal field theory
(CFT) are nothing but the integral kernels of intertwining operators for two
equivalent representations of conformal algebra. Such intertwining operators
are known to fulfill some operator identities---the intertwining relations---in
the representation space of conformal algebra. Meanwhile, it has been known
that the S-matrix operator in scattering theory is nothing but the intertwining
operator between the Hilbert spaces of in- and out-particles. Inspired by this
algebraic resemblance, in this paper we develop a simple Lie-algebraic approach
to momentum-space two-point functions of thermal CFT living on the hyperbolic
spacetime $\mathbb{H}^{1}\times\mathbb{H}^{d-1}$ by exploiting the idea of
Kerimov's intertwining operator approach to exact S-matrix. We show that in
thermal CFT on $\mathbb{H}^{1}\times\mathbb{H}^{d-1}$ the intertwining
relations reduce to certain linear recurrence relations for two-point functions
in the complex momentum space. By solving these recurrence relations, we obtain
the momentum-space representations of advanced and retarded two-point functions
as well as positive- and negative-frequency two-point Wightman functions for a
scalar primary operator in arbitrary spacetime dimension $d\geq3$.
