  We study the heat transport of S = 1/2 chain compound
CuCl_2$\cdot$2((CH_3)_2SO) along the b axis (vertical to the chain direction)
at very low temperatures. The zero-field thermal conductivity (\kappa) shows a
distinct kink at about 0.9 K, which is related to the long-range
antiferromagnetic (AF) transition. With applying magnetic field along the c
axis, \kappa(H) curves also show distinct changes at the phase boundaries
between the AF and the high-field disordered states. These results indicate a
strong spin-phonon interaction and the magnetic excitations play a role in the
b-axis heat transport as phonon scatterers.
