Classroom observation protocols standardize the assessment of teaching effectiveness and facilitate comprehension of classroom interactions. Whereas these protocols offer teachers specific feedback on their teaching practices, the manual coding by human raters is resource-intensive and often unreliable. This has sparked interest in developing AI-driven, cost-effective methods for automating such holistic coding. Our work explores a multimodal approach to automatically estimating encouragement and warmth in classrooms, a key component of the Global Teaching Insights (GTI) study's observation protocol. To this end, we employed facial and speech emotion recognition with sentiment analysis to extract interpretable features from video, audio, and transcript data. The prediction task involved both classification and regression methods. Additionally, in light of recent large language models' remarkable text annotation capabilities, we evaluated ChatGPT's zero-shot performance on this scoring task based on transcripts. We demonstrated our approach on the GTI dataset, comprising 367 16-minute video segments from 92 authentic lesson recordings. The inferences of GPT-4 and the best-trained model yielded correlations of r = .341 and r = .441 with human ratings, respectively. Combining estimates from both models through averaging, an ensemble approach achieved a correlation of r = .513, comparable to human inter-rater reliability. Our model explanation analysis indicated that text sentiment features were the primary contributors to the trained model's decisions. Moreover, GPT-4 could deliver logical and concrete reasoning as potential teacher guidelines. Our findings provide insights into using advanced, multimodal techniques for automated classroom observation, aiming to foster teacher training through frequent and valuable feedback.