The study examined the degradation process of various types of polymers used to form models using the fused deposition modeling (FDM) and three-dimensional printing (3DP) methods and used in the investment casting method. Commercial filaments made of polylactide (PLA), acrylonitrile butadiene styrene terpolymer (ABS), high-impact polystyrene (HIPS), polyamide 12 (PA12), poly(methyl methacrylate) (PMMA), and polypropylene (PP) were used to produce gypsum molds. The assessment included organic volatile compounds (VOCs) released during mold heating and model degradation, which is characteristic of this technological process. The screening qualitative chromatographic analysis of decomposition products sampled from various points of the production hall made it possible to define potential threats related to the processing of selected polymers and the necessary preventive measures. Furthermore, passive diffusion-type samplers were used at the sampling stage of VOCs emitted to the gaseous phase to reduce nuisance and user interference. Studies have been completed to characterize the thermoplastic polymer degradation process. The coupled thermogravimetry (TGA) with analysis of gaseous products by infrared spectroscopy with Fourier transformation (FT-IR) has been used. The presented results are the first to compare and rate the use of this still-developing novel aspect of castings by the method of fused models.