Is the Sampling Temperature the Agent’s Decision State? A Reference-Based Indicator and Its Comparison with Entropy, Calibration and Semantic Entropy

Operators of large language model (LLM) agents control reliability mainly through the sampling temperature, yet the temperature that governs an agent’s choices may differ from the one that was set. We define the effective decision temperature, T_eff, as the temperature at which an agent’s chosen tokens are best explained by a reference valuation computed on a clean copy of the context and state when it is identified. Using a synthetic agent and four open-weight models from three families on ordered-list tasks with a planted off-path attractor of graded strength, we test three hypotheses and compare T_eff with token entropy, confidence, expected calibration error (ECE) and a discrete semantic entropy. Accuracy rose and then fell with temperature for attractors of intermediate strength, peaking near T = 2 to 2.5 on the alphabet task, whereas weak attractors declined monotonically. Pressure raised T_eff in Qwen2.5-3B (5 of 7 identified matched cells) but not in Llama-3.2-3B (1 of 8); contamination had little effect. As a detector of distorted contexts, T_eff flagged 6 of 15 pressured cells, against 10 of 16 for entropy and 13 of 16 for label-dependent ECE. All label-free indicators computed from the agent’s own history missed fully locked-in trajectories, whereas a reference computed on a de-duplicated history, which needs no labels, flagged all 25 locked cells. T_eff is best treated as a model-specific diagnostic, not a general-purpose monitor. In a revision study with four further small models (from 0.5 to 1.7 billion parameters, three families, one inference stack), three wordings of each distortion, full-vocabulary generation and entailment-clustered semantic entropy, T_eff again did not outperform simpler indicators, and with six choices per trajectory its 95% interval spanned a median factor of about 9.