Current Large Language Models (LLMs) demonstrate exceptional generative capabilities but lack a coherent "inner life", failing to model the dynamics of emotion regulation essential for believable affective behavior. Constrained by statelessness and a lack of theoretical grounding, standard models struggle to maintain psychological depth. To address this, we propose a computational cognitive-affective architecture grounded in Dual-Process Theory. Our system computationally distinguishes between visceral emotional reaction (Appraisal) and strategic verbal expression (Formulation), effectively operationalizing the gap between "feeling" and "saying". This modular design allows agents to embody specific personas by integrating long-term memory, dynamic emotional states, personality and goals. We evaluated the system in simulated narrative scenarios using an LLM-as-a-judge protocol. We frame this system as a computational experiment to investigate the mechanics of artificial affect. Results confirm the feasibility of simulating a coherent and believable inner emotional monologue. However, analysis in high-pressure scenarios reveals a rational bias where strategic planning can override this emotional authenticity. These findings contribute to Computational Affective Science by demonstrating that while cognitive sequentiality successfully generates inner lives, enforcing affective primacy in the decision cycle is critical to prevent excessive rational regulation.