Artificial intelligence (AI) applications, including advanced machine learning (ML), have received attention in education, and generative AI-powered chatbots like ChatGPT and Copilot have been adopted in diverse educational settings worldwide. However, the actual use of and perception regarding AI-powered chatbots by learners have been under-investigated. Obtaining a more accurate understanding of learners’ perceptions, particularly their trust in AI-powered technology, is crucial for preparing for future education because learners’ trust in the technology itself is significantly related to successful technology adoption in various educational contexts. To address this issue, we focused on undergraduate students’ trust in AI-powered chatbots within their courses and investigated the relationship between their trust levels and learning performance. Additionally, we explored the potential association between learners’ trust levels, self-regulated learning, and computational thinking skills. This research employed an exploratory study design with a regular course setting, and there were no experimental treatments involved. In the results, we found that learners’ trust levels were not correlated with their computational thinking, self-regulated learning, or learning performance. Furthermore, these constructs (i.e., self-regulated learning, computational thinking, and learning performance) did not significantly predict learners’ trust in AI. However, there was a notable difference between high and low performers concerning changes in trust over time. Trust levels among low performers exhibited a significant change over the semester, whereas those of high performers remained relatively stable. The study suggests that expectations regarding trusting generative AI technology can be influenced by trusting intention through performance.