Abstract: The bolometric response of YBa₂Cu₃O_7-δ(YBCO) hot-electron bolometers (HEBs) to near-infrared radiation was studied. Devices were fabricated from a 50 nm thick film and had in-plane areas of 10 × 10 µm2, 2 × 0.2 µm2, 1 × 0.2µm2 and 0.5 × 0.2 µm2. We found that nonequilibrium phonons cool down more effectively for the bolometers with smaller area. For the smallest bolometer the bolometric component in the response is 10 dB less than for the largest one.