We present a study of a cold-electron bolometer operating at 350 mK with a twin-slot antenna coupling radiation at 160 GHz. The detector's absorbing element consists of degenerately-doped strained silicon and has Schottky contacts to superconducting aluminium leads. These contacts allow for direct electron cooling of the absorber to below the phonon temperature, enabling the cold-electron bolometer to achieve much faster time constants (τ < 1 μs) compared to conventional bolometric detectors while not sacrificing sensitivity. We measure both the dark and optically-loaded noise of the detector via a novel method of cross-correlating the outputs of two amplifiers in order to measure noise below the amplifier noise level. From this we measure the photon-noise limited noise-equivalent power of the detector to be 6.6 × 10-17 W Hz-1/2 when observing a 77-Kelvin source.