The longitudinal thermal conductivity of a unidirectional fibre-reinforced composite containing an array of equally spaced transverse matrix cracks is calculated. The cracked composite is modelled by a cylindrical cell which accounts for altered heat transfer across the matrix cracks as well as through debonded portions of the fibre-matrix interface. Heat transfer mechanisms across the cracks and dedonded interfaces considered are contact, gaseous conduction, and radiation, and the relative importance of these mechanisms is discussed. Approximate closed form solutions to the cell model for the overall thermal conductivity are obtained using an approach reminiscent of the shear lag analysis of stiffness loss due to matrix cracking and debonding. Selected numerical results from a finite-element analysis of the cell model are presented to complement the analytical solutions. Both matrix cracking and interfacial debonding have the potential for significantly reducing the longitudinal thermal conductivity.