The thermal field around a partially debonded spherical particle, having a spherical-cap crack, embedded in an infinite matrix is presented. Heat flow parallel and perpendicular to the axis of symmetry is considered. When the conductivity of the particle is equal to that of the matrix the results of the present analysis agree with previously published results. An estimate for the effective thermal conductivity of a dispersion of these particles is presented. (c) 2006 Elsevier Ltd. All rights reserved.