Sources of internal and external noise in submillimeter detectors based on bolometers with hot electrons are investigated. The contributions of the thermal background radiation and bolometer response are analyzed at various temperatures and background levels. The shot noise suppression factor is estimated as a function of the ratio between the bolometer length and characteristic lengths of electron-electron and electron-phonon relaxation. Experimental data on bolometer noise at various temperatures are presented. Noise spectra, the noise-equivalent power, and the response of the submillimeter bolometer detector to the input signal are measured.