Microrefrigerators based on normal metal-insulator-superconductor (NIS) junctions represent a very attractive alternative to cool the microbolometers and calorimeters for astrophysical observations in space-borne experiments. The performance in such measurements requires a good knowledge of the noise sources in the detectors. In this paper we present detailed calculations of the thermal fluctuations and of the noise equivalent power due to the heat transfer through the NIS junctions or the thermal contact between different subsystems of the detector. The influence of the input optical power - which, in the cases that interest us, is the cosmic background radiation - will also be evaluated. Analytical approximations valid at low temperatures are given.