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The operation of the hot-electron bolometer with normal metal-insulator-superconductor (NIS) tunnel junction as a temperature sensor is analyzed theoretically. The responsivity and the noise equivalent power (NEP) of the bolometer are obtained numerically for typical experimental parameters. Relatively simple approximate analytical expressions for these values are derived. The time constant of the device is also found. We demonstrate that the effect of the electron cooling by the NIS junction, which serves as a thermometer, can improve the sensitivity. This effect is also useful in the presence of the finite background power load. We discuss the effect of the correlation of the shot noise and the heat flow noise in the NIS junction. © 2001 American Institute of Physics.