This paper presents a method for evaluating the risk of autoignition for the canonical problem of an enclosed hydrogen jet in crossflow (JICF), which is highly relevant to the design of mixing ducts. The proposed method is based on the separation of the underlying mixing pattern from the evolution of the chemical reactions, whereas the effect of mixing is maintained on the latter with the purpose of creating a reliable yet computationally efficient design tool for hydrogen gas turbines. Two variants of the incompletely stirred reactor network (ISRN) approach are proposed that provide the evolution of preignition radicals and autoignition kernel location, leveraging a nonreacting computational fluid dynamics solution or an analytical mixing pattern. The ISRN governing equations include all the salient features of hydrogen transport and lead to a conservative estimate of autoignition risk. Application to a few model problems with varied operating conditions suggests that radical buildup in the JICF can lead to autoignition in the vicinity of a most reactive mixture fraction, which is consistent with other laminar or turbulent hydrogen flows. However, the radical formation and autoignition kernel location strongly depend on the prediction of the underlying mixing field and the amount of differential diffusion within the JICF, which here primarily favors lower values of the composite mixture fraction and the transport of hydrogen and radicals away from the jet trajectory.