Two-dimensional electrothermal crack problems are treated. Steady temperature distribution near the lip of a crack is analyzed for a homogeneous isotropic conductive material with the steady dc current. A path-independent integral jtis newly introduced and is used for the analysis together with the jeintegral, which has been introduced by the authors for electric crack problems. Based on the analysis, the mode it stress intensity factor KII, which is attributed to thermal stresses caused by Joule heating, is shown to be a function of the two path-independent integrals.