Artificial Emotional Intelligence (AEI) enables conversational agents (CAs) to recognize and respond to human emotions, improving user interaction. This study examines how AEI influences satisfaction through trust and anthropomorphism in a customer service chatbot setting. We propose that AEI not only builds trust directly but also increases perceived human-likeness, which further impacts satisfaction. Using a between-subjects experiment, participants will engage with High vs. Low AEI CAs. Trust, satisfaction, and anthropomorphism will be measured using validated scales. Findings will offer insights into the design of emotionally intelligent, user-centric AI systems and inform future work across multiple CA modalities.