Conceptual metaphor detection is a well-researched topic in Natural Language Processing. At the same time, conceptual metaphor use analysis produces unique insight into individual psychological processes and characteristics, as demonstrated by research in cognitive psychology. Despite the fact that state-of-the-art language models allow for highly effective automatic detection of conceptual metaphor in benchmark datasets, the models have never been applied to psychological tasks. The benchmark datasets differ a lot from experimental texts recorded or produced in a psychological setting, in their domain, genre, and the scope of metaphoric expressions covered.We present the first experiment to apply NLP metaphor detection methods to a psychological task, specifically, analyzing individual differences. For that, we annotate MetPersonality, a dataset of Russian texts written in a psychological experiment setting, with conceptual metaphor. With a widely used conceptual metaphor annotation procedure, we obtain low annotation quality, which arises from the dataset characteristics uncommon in typical automatic metaphor detection tasks. We suggest a novel conceptual metaphor annotation procedure to mitigate issues in annotation quality, increasing the inter-annotator agreement to a moderately high level. We leverage the annotated dataset and existing metaphor datasets in Russian to select, train and evaluate state-of-the-art metaphor detection models, obtaining acceptable results in the metaphor detection task. In turn, the most effective model is used to detect conceptual metaphor automatically in RusPersonality, a larger dataset containing meta-information on psychological traits of the participant authors. Finally, we analyze correlations of automatically detected metaphor use with psychological traits encoded in the Freiburg Personality Inventory (FPI).Our pioneering work on automatically-detected metaphor use and individual differences demonstrates the possibility of unprecedented large-scale research on the relation between of metaphor use and personality traits and dispositions, cognitive and emotional processing.