A new approach to obtaining the energy criterion for the fracture of a thermoelastic body with a growing crack has been put forward. The criterion is based directly on the first and second laws of thermodynamics. An analysis was restricted by brittle quasi-static fracture processes in the weakly nonuniform temperature field (WNUTF). The Griffith conception of surface energy supplemented by the temperature dependence of this energy was used. No thermodynamic fluxes were shown to arise in the WNUTF, except for the rate of a growing crack. This result made it possible to extend the Griffith criterion to the nonisothermal case. The vectorial J-integral representing the energy flux vector at the crack tip was established to be the only fracture parameter for thermoelastic media with cracks. Different energy flux vector representation forms for cases of linear and nonlinear thermoelasticity were considered and discussed.