The longitudinal component of the electronic thermal conductivity kappa(xx) in a superconducting vortex state is calculated as a function of magnetic field B. Calculations are performed by taking account of the spatial dependence of normal Green's function g, which was neglected in the previous studies using the Brandt-Pesch-Tewordt method. We discuss the possibility of using kappa(xx)(B) as a probe of the pair potential symmetry. (C) 2007 Elsevier B.V. All rights reserved.