Temperature changes near the end of a curvilinear cohesive crack and their influence on crack growth are investigated. The problem of local temperature changes consists in a delay or retardation of the cohesive crack growth. The bonds between the curvilinear crack faces in the end zones are modeled by application to the crack surface cohesive forces caused by the presence of bonds. The boundary value problem of equilibrium of the curvilinear crack with interfacial bonds in the end zones under action of external tensile loads, induced temperature field and tractions in the bonds preventing to its opening, is reduced to a system of singular integral equations with a Cauchy-type kernel. From the solution of this equation system, normal and tangential tractions in the bonds are found. Analysis of the limit equilibrium of the crack using the end zone model is performed on the basis of a criterion of bonds limiting stretching and includes: 1) establishment of tractions depending on opening of the crack faces; 2) evaluation of the stress state near the curvilinear crack with taking into account tensile loads, induced temperature field, tractions in the bonds; 3) determination of the critical external tensile loads.