The thermal conductivity of a diacetylene monomer has been measured over the temperature range 2.8-25 K. The data are found to have a temperature dependence and magnitude very close to those previously obtained for the polymer form of the diacetylene. It is shown that the data support the model of acoustic phonon scattering by low energy optical modes associated with the side groups. The optical mode energies have been determined by far-infrared spectroscopy and it is shown that by using these values to model the data a good fit is obtained with each mode having an acoustic-optical phonon coupling of 6.3 meV.