Issue tracking systems enable users and developers to comment on problems plaguing a software system. Empirical Software Engineering (ESE) researchers study (open-source) project issues and the comments and threads within to discover---among others---challenges developers face when, e.g., incorporating new technologies, platforms, and programming language constructs. However, issue discussion threads accumulate over time and thus can become unwieldy, hindering any insight that researchers may gain. While existing approaches alleviate this burden by classifying issue thread comments, there is a gap between searching popular open-source software repositories (e.g., those on GitHub) for issues containing particular keywords and feeding the results into a classification model. In this paper, we demonstrate a research infrastructure tool called QuerTCI that bridges this gap by integrating the GitHub issue comment search API with the classification models found in existing approaches. Using queries, ESE researchers can retrieve GitHub issues containing particular keywords, e.g., those related to a certain programming language construct, and subsequently classify the kinds of discussions occurring in those issues. Using our tool, our hope is that ESE researchers can uncover challenges related to particular technologies using certain keywords through popular open-source repositories more seamlessly than previously possible. A tool demonstration video may be found at: https://youtu.be/fADKSxn0QUk.