Micromachined Joule-Thomson coolers can be used for cooling small electronic devices. However, a critical issue for long-term operation of these microcoolers is the clogging caused by the deposition of water that is present as impurity in the working fluid. We present a model that describes the deposition process considering diffusion and kinetics of water molecules. In addition, the deposition and sublimation process was imaged, and the experimental observation fits well to the modeling predictions. By changing the temperature profile along the microcooler, the operating time of the microcooler under test at 105 K extends from 11 to 52 h.