This article demonstrates the improvement of antenna-coupled field-effect transistor detection sensitivity at 540 GHz as temperature reduces to 20 K with noise-equivalent power (NEP) comparable to superconducting niobium transition-edge sensors at 4 K. This FET sensor approach enables space-based and payload-constrained applications with liquid nitrogen cooling where deep cryogenic cooling is impractical. A 2.85 THz power sensing system for spectroscopy applications with an 8x8 pixel-binned detector array was fabricated and evaluated from 20-300 K. The system achieved 67 dB linear dynamic range without saturation for 1-Hz detection bandwidth with a -3 dB readout bandwidth of 5 MHz.