Current and future experiments observing the cosmic microwave background require a detailed understanding of optical performance at cryogenic temperatures. Pre-deployment analysis of optics can be performed in custom-engineered cryogenic test beds, such as Mod-Cam, a first light camera for the CCAT project. This work presents studies of the mechanical and thermal performance of CryoSim, a model of a generic cylindrical 4-K cryostat cooled with a commercial pulse tube cryocooler that can be used to characterise optical components and full reimaging optical systems. CryoSim is extensively parametrised, allowing the joint analysis and optimisation of mechanical and thermal performance via finite element methods. Results from this model are validated against measured cooldown data of the Mod-Cam cryostat. Due to the extensive parametrisation of the model, significant modifications of the cryostat geometry may be implemented to be representative of any system the scientific community may desire, and validation of thermal and mechanical performance can be carried out rapidly.