Distributed fire-monitoring systems may involve many sensing devices reporting over a shared uplink, even though the operational objective is often to identify regions exhibiting evidence of fire rather than to recover device-specific measurements. We introduce TERRA (Task-Oriented Edge Representation and Regional Aggregation), an edge-AI framework that combines task-oriented local inference, identity-free region-tagged reporting, and permutation-invariant regional evidence aggregation. TERRA supports two reporting modes: TERRA-Score, in which each device communicates a quantized local fire probability, and TERRA-Feature, in which it communicates a compact learned representation for receiver-side aggregation using a permutation-invariant DeepSets model. Using all 15 numerical sensing modalities of the distributed indoor EN54 fire-alarm dataset as a proof-of-concept testbed, we evaluate regional inference for an episode-level fire-scenario target under repetition-disjoint three-fold cross-validation. We study representation size, task-payload quantization, report availability, and robustness to missed and false recovered messages. With nine reports and perfect message recovery, TERRA-Feature achieves mean AUPRC 0.990 using a 24-bit task payload, while TERRA-Score achieves 0.987 using only 6 bits; both attain an MDR of 1.81% at FAR $\leq$1%. TERRA-Feature achieves slightly higher AUPRC under reliable recovery, whereas the more compact TERRA-Score is less sensitive to increasing false-message contamination.