Time-series forecasting is fundamental in industrial domains like manufacturing and smart factories. As systems evolve toward automation, models must operate on edge devices (e.g., PLCs, microcontrollers) with strict constraints on latency and memory, limiting parameters to a few thousand. Conventional deep architectures are often impractical here. We propose the Fourier-Efficient Adaptive Temporal Hierarchy Forecaster (FEATHer) for accurate long-term forecasting under severe limits. FEATHer introduces: (i) ultra-lightweight multiscale decomposition into frequency pathways; (ii) a shared Dense Temporal Kernel using projection-depthwise convolution-projection without recurrence or attention; (iii) frequency-aware branch gating that adaptively fuses representations based on spectral characteristics; and (iv) a Sparse Period Kernel reconstructing outputs via period-wise downsampling to capture seasonality. FEATHer maintains a compact architecture (as few as 400 parameters) while outperforming baselines. Across eight benchmarks, it achieves the best ranking, recording 60 first-place results with an average rank of 2.05. These results demonstrate that reliable long-range forecasting is achievable on constrained edge hardware, offering a practical direction for industrial real-time inference.