This article presents a comprehensive methodology to monitor internal team climate in agile educational projects. The proposed approach integrates Peer Assessment, Process Evaluation, and Product Assessment using the Analytic Hierarchy Process (AHP) to calculate a dynamic Internal Team Climate Index (ITCI). Designed for Scrum-based project courses, the methodology enables instructors to identify behavioral patterns, anticipate potential dysfunctions, and guide effective pedagogical interventions. A case study involving 25 student teams over three sprints was conducted to validate the framework. Results show a strong correlation between early collaboration metrics and final team performance, with statistical evidence confirming significant improvements over time. The ITCI not only quantifies team dynamics but also offers a practical tool for formative assessment and continuous improvement in software engineering education. Survey data from 94 students further confirmed the framework's perceived fairness, formative value, and motivational impact. The proposed methodology is validated in a Scrum-based software engineering course and demonstrates potential adaptability to similar educational contexts. Rather than constituting a purely psychological climate instrument, the Internal Team Climate Index (ITCI) is conceived as a formative composite indicator that integrates peer-perceived climate with process- and product-related contextual proxies.