Analytical relations for temperature response of the bolometer to periodic radiation pulses are obtained. It is theoretically shown and experimentally confirmed by the example of infrared bolometers that when detecting short radiation pulses, in contrast to the case of constant radiation, increasing the thermal conductivity of the bolometer and, accordingly, decreasing its thermal relaxation time, it is possible to significantly increase the response rate of the receiver, practically without reducing its sensitivity. The possibility of effective registration of pulsed terahertz radiation by microbolometers with a resistively coupled, thermally non-isolated antenna is considered. It is shown that such bolometers, which have increased thermal conductivity and, accordingly, reduced sensitivity to continuous-wave radiation, can be highly effective when detecting pulsed radiation with a duration shorter than the thermal relaxation time of the bolometer. On their basis, uncooled matrix detectors of pulsed terahertz radiation, characterized by a minimum detectable energy of less than 110-12 J and a frame rate of up to 1000 Hz, can be developed.