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TolTEC is an upcoming millimeter-wave imaging polarimeter designed to fill the focal plane of the 50-m-diameter Large Millimeter Telescope (LMT). Combined with the LMT, TolTEC will offer high-angular-resolution (5–10 ) simultaneous, polarization-sensitive observations in three wavelength bands: 1.1, 1.4, and 2.0 mm. Additionally, TolTEC will feature mapping speeds greater than 2 deg2∕mJy2∕h , thus enabling wider surveys of large-scale structure, galaxy evolution, and star formation. These improvements are only possible through the integration of approximately 7000 low-noise, high-responsivity superconducting Lumped Element Kinetic Inductance Detectors. Utilizing three focal planes of detector arrays requires the design, fabrication, and characterization of a unique, large-scale cryogenic system. Based on thermal models and expected photon loading, the focal planes must have a base operational temperature below 150 mK. To achieve this base temperature, TolTEC utilizes two cryocoolers, a Cryomech pulse tube cooler and an Oxford Instruments dilution refrigerator, to establish four thermal stages: 45 K, 4 K, 1 K, and 100 mK. During the design phase, we developed an object-oriented Python code to model the heat loading on each stage as well as the thermal gradients throughout the system. This model has allowed us to improve thermal gradients in the system as well as locate areas of poor thermal conductivity prior to ending a cooldown. The results of our model versus measurements from our cooldowns will be presented along with a detailed overview of TolTEC’s cryogenic system. We anticipate TolTEC to be commissioned at the LMT by Spring 2020.