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International audience; The Simons Observatory (SO) will provide precision polarimetry of the cosmic microwave background (CMB) using a series of telescopes which will cover angular scales from arc-minutes to tens of degrees, contain over 60,000 detectors, and observe in frequency bands between 27 GHz and 270 GHz. SO will consist of a six-meter-aperture telescope initially coupled to roughly 35,000 detectors along with an array of half-meter aperture refractive cameras, coupled to an additional 30,000+ detectors. The large aperture telescope receiver (LATR) is coupled to the SO six-meter crossed Dragone telescope and will be 2.4 m in diameter, weigh over 3 metric tons, and have five cryogenic stages (80 K, 40 K, 4 K, 1 K and 100 mK). The LATR is coupled to the telescope via 13 independent optics tubes containing cryogenic optical elements and detectors. The cryostat will be cooled by two Cryomech PT90 (80 K) and three Cryomech PT420 (40 K and 4 K) pulse tube cryocoolers, with cooling of the 1 K and 100 mK stages by a commercial dilution refrigerator system. The secondo component, the small aperture telescope (SAT), is a single optics tube refractive cameras of 42 cm diameter. Cooling of the SAT stages will be provided by two Cryomech PT420, one of which is dedicated to the dilution refrigeration system which will cool the focal plane to 100 mK. SO will deploy a total of three SATs. In order to estimate the cool down time of the camera systems given their size and complexity, a finite difference code based on an implicit solver has been written to simulate the transient thermal behavior of both cryostats. The result from the simulations presented here predict a 35 day cool down for the LATR. The simulations suggest additional heat switches between stages would be effective in distribution cool down power and reducing the time it takes for the LATR to reach its base temperatures. The SAT is predicted to cool down in one week, which meets the SO design goals.