Internet-based cognitive behavioral therapy (iCBT) offers a scalable, cost-effective, accessible, and low-threshold form of psychotherapy. Recent advancements explored the use of conversational agents such as chatbots and voice assistants to enhance the delivery of iCBT. These agents can deliver iCBT-based exercises, recognize and track emotional states, assess therapy progress, convey empathy, and potentially predict longterm therapy outcome. However, existing systems predominantly utilize categorical approaches for emotional modeling, which can oversimplify the complexity of human emotional states. To address this, we developed a transformer-based model for dimensional text-based emotion recognition, fine-tuned with a novel, comprehensive dimensional emotion dataset comprising 75,503 samples. This model significantly outperforms existing state-of-the-art models in detecting the dimensions of valence, arousal, and dominance, achieving a Pearson correlation coefficient of r =0:90, r = 0:77, and r =0:64, respectively. Furthermore, a feasibility study involving 20 participants confirmed the model's technical effectiveness and its usability, acceptance, and empathic understanding in a conversational agent-based iCBT setting, marking a substantial improvement in personalized and effective therapy experiences.