AI models of equivalent capability can exhibit fundamentally different behavioral patterns, yet no standardized instrument exists to measure these dispositional differences. Existing approaches either borrow human personality dimensions and rely on self-report (which diverges from actual behavior in LLMs) or treat behavioral variation as a defect rather than a trait. We introduce the Model Temperament Index (MTI), a behavior-based profiling system that measures AI agent temperament across four axes: Reactivity (environmental sensitivity), Compliance (instruction-behavior alignment), Sociality (relational resource allocation), and Resilience (stress resistance). Grounded in the Four Shell Model from Model Medicine, MTI measures what agents do, not what they say about themselves, using structured examination protocols with a two-stage design that separates capability from disposition. We profile 10 small language models (1.7B-9B parameters, 6 organizations, 3 training paradigms) and report five principal findings: (1) the four axes are largely independent among instruction-tuned models (all |r| < 0.42); (2) within-axis facet dissociations are empirically confirmed -- Compliance decomposes into fully independent formal and stance facets (r = 0.002), while Resilience decomposes into inversely related cognitive and adversarial facets; (3) a Compliance-Resilience paradox reveals that opinion-yielding and fact-vulnerability operate through independent channels; (4) RLHF reshapes temperament not only by shifting axis scores but by creating within-axis facet differentiation absent in the unaligned base model; and (5) temperament is independent of model size (1.7B-9B), confirming that MTI measures disposition rather than capability.