The paper begins by exploring the rationality of ethical trust as a foundational concept. This involves distinguishing between trust and trustworthiness and delving into scenarios where trust is both rational and moral. It lays the groundwork for understanding the complexities of trust dynamics in decision-making scenarios. Following this theoretical groundwork, we introduce an agent-based simulation framework that investigates these dynamics of ethical trust, specifically in the context of a disaster response scenario. These agents, utilizing emotional models like Plutchik's Wheel of Emotions and memory learning mechanisms, are tasked with allocating limited resources in disaster-affected areas. The model, which embodies the principles discussed in the first section, integrates cognitive load management, Big Five personality traits, and structured interactions within networked or hierarchical settings. It also includes feedback loops and simulates external events to evaluate their impact on the formation and evolution of trust among agents. Through our simulations, we demonstrate the intricate interplay of cognitive, emotional, and social factors in ethical decision-making. These insights shed light on the behaviors and resilience of trust networks in crisis situations, emphasizing the role of rational and moral considerations in the development of trust among autonomous agents. This study contributes to the field by offering an understanding of trust dynamics in socio-technical systems and by providing a robust, adaptable framework capable of addressing ethical dilemmas in disaster response and beyond. The implementation of the algorithms presented in this paper is available at this GitHub repository: \url{https://github.com/abbas-tari/ethical-trust-cognitive-modeling}.