Emotion recognition is a fundamental component of next-generation human-computer interaction (HCI), enabling machines to perceive, understand, and respond to users' affective states. However, existing systems often rely on single-modality analysis such as facial expressions, speech tone, or textual sentiment, resulting in limited robustness and poor generalization in real-world environments. To address these challenges, this study proposes a Cloud-Based Cross-Modal Transformer (CMT) framework for multimodal emotion recognition and adaptive human-computer interaction. The proposed model integrates visual, auditory, and textual signals using pretrained encoders (Vision Transformer, Wav2Vec2, and BERT) and employs a cross-modal attention mechanism to capture complex interdependencies among heterogeneous features. By leveraging cloud computing infrastructure with distributed training on Kubernetes and TensorFlow Serving, the system enables scalable, low-latency emotion recognition for large-scale user interactions. Experiments conducted on benchmark datasets including IEMOCAP, MELD, and AffectNet demonstrate that the CMT achieves state-of-the-art performance, improving the F1-score by 3.0 percent and reducing cross-entropy loss by 12.9 percent compared to strong multimodal baselines. Additionally, cloud deployment evaluations show an average response latency of 128 ms, representing a 35 percent reduction compared with conventional transformer-based fusion systems. These results confirm that the proposed framework enables efficient, real-time emotion recognition and adaptive feedback in applications such as intelligent customer service, virtual tutoring systems, and affective computing interfaces, marking an important step toward cloud-native affective computing and emotionally intelligent interactive systems.