Tight-Setting Alternatives for Long-Horizon Building Temperature Prediction: Bilinear Imputation and Multi-Scale Encoding under Sensor Uncertainty

We evaluate two tight-setting alternatives within Seasonal-PINN V3, a hybrid XGBoost-PINN with adaptive physics weighting, on Google SB1 (123 zones, 32.2M readings, 28.6% missing): (1) bilinear interpolation - zero-training, O(1) additional working memory with respect to the number of zones, ~66× faster than LightGBM - and (2) TimeMixer PDM as a multi-scale encoder. Bilinear Variant A and B produce identical downstream MAE, revealing that neither evaluated spatial ordering provided measurable downstream benefit at 5-minute resolution. With imputation-aware weighting (w=0.3/1.0), bilinear fully recovers the LightGBM quality gap (0.151°F at S4). TimeMixer without weights collapses at 2-year horizons (S11: 12.030°F) but with weights achieves best weighted S7 MAE (0.317°F) - suggesting that physics-informed weighting has a stronger effect on long-horizon stability than encoder choice within the evaluated configurations. These findings are directly relevant to resource-constrained Building Management Systems (BMS) prevalent across Africa and the Global South, where per-zone model storage, training latency, and inference memory represent hard deployment constraints.