LLM-based multi-agent systems (MAS) show promise on complex tasks but remain prone to coordination failures such as goal drift, error cascades, and misaligned behaviors. We propose Explicit Trait Inference (ETI), a psychologically grounded method for improving coordination. ETI enables agents to infer and track partner characteristics along two established psychological dimensions--warmth (e.g., trust) and competence (e.g., skill)--from interaction histories to guide decisions. We evaluate ETI in controlled settings (economic games), where it reduces payoff loss by 45-77%, and in more realistic, complex multi-agent settings (MultiAgentBench), where it improves performance by 3-29% depending on the scenario and model, relative to a CoT baseline. Additional analysis shows that gains are closely linked to trait inference: ETI profiles predict agents' actions, and informative profiles drive improvements. These results highlight ETI as a lightweight and robust mechanism for improving coordination in diverse multi-agent settings, and provide the first systematic evidence that LLM agents can (i) reliably infer others' traits from interaction histories and (ii) leverage structured awareness of others' traits for coordination.