The Beremin model can handle both the plastic constraint effect and data scatter for brittle fracture. Many researchers have been investigating its applicability for more than 30 years and are still discussing the temperature dependence of Weibull parameters used in this model. The authors have already presented the experimental and analytical investigation results for low alloy steel using C(T) specimens in several temperature conditions. The analysis suggested that the Weibull parameters are constant for temperature. In this paper fracture toughness tests of carbon steel using SE(B) specimens at −120°C and −50°C were performed and the Weibull parameters were determined by the test results at −120°C. KJc of the 5% lower bound and the 95% upper bound confidence limit at −50°C were predicted using the Weibull parameters from −120°C. As a result, the predicted 5% lower bound confidence limit was close to the lowest experimental KJc value, whose fracture mode was nearly cleavage fracture. This means there is no temperature dependency of the Weibull parameters and the results are similar to those of low alloy steel. On the other hand the predicted 95% upper bound confidence limit had a large gap when compared with the experimental upper KJc value. One of the reasons of large gap was estimated that the parameter fitting of the GTN model was performed without consideration of the parameters relating to the second void effect and a precise stress-strain field after a large ductile crack growth with several millimeters was not obtained.