CLIL (Content and Language Integrated Learning) is a teaching method in which learners develop linguistic competence and problem-solving abilities by learning content subjects in another language. However, learners' cognitive gains may depend on their affectivity. Negative affect hampers complex cognitive processing essential for problem-solving, while experiences of failed intellectual effort may lead to impaired information processing called intellectual helplessness (IH) (Sedek and McIntosh 1998). Negative affectivity among children in CLIL programmes may be caused by ill-managed classes and linguistically inadequate materials (Otwinowska 2013). Here, we explore links between affectivity and cognition in upper-primary Polish children (N = 140) who learn mathematics and science in English. To that end, we use qualitative and quantitative measures to verify whether negative emotions inhibit cognitive processes. Children completed an anonymous attitude survey and the IH Scale (Sedek 1995) to investigate their affective state and symptoms of cognitive demobilization (inhibition in active problem-solving). We also obtained children's term grades in mathematics, science and English to investigate possible relationships between children's accomplishments in those subjects and their affective responses to the CLIL modules. The study reveals symptoms of IH and negative affectivity experienced by young CLIL learners. The significant predictors of IH in the CLIL classes are negative affectivity and grades in science and mathematics. Nonetheless, grades in English do not significantly predict IH in CLIL. We explain this paradox in terms of different types of language needed in general English and CLIL classes: basic interpersonal communication skills vs. cognitive academic language proficiency (Cummins 1979).