Cognitive empathy, the ability to imagine and anticipate the mental states of others, is a fundamental human ability, essential in design-thinking-based problem-solving. While conversational generative AI systems hold promise for enhancing human performance, their impact on cognitive processes remains underexplored. This study examines how such AI systems influence cognitive empathy in a higher education context. Twenty-two students from design-focused programs participated in creative problem-solving of a wicked societal problem, with half of the sample interacting with a conversational generative AI system. Using a mixed-method approach - comprising self-report surveys, interviews, and retrospective think-aloud protocols - this study reveals that AI-assisted solution generation may diminish internal thought processes and significantly affect the fantasy dimension of cognitive empathy. These insights are particularly relevant for researchers and practitioners advancing and applying human-AI collaboration in creative and educational contexts, highlighting implications for human creativity from the cognitive lens of fantasy.