In the automotive sector, the use of nonwoven preforms consisting of natural and thermoplastic fibers processed by compression molding is well known to manufacture vehicle interior parts. Although these natural fiber composites (NFCs) have undeniable advantages (lightweight, good life cycle assessment, recyclability, etc.), the latter release volatile organic compounds (VOCs) and odors inside the vehicle interior, which remain obstacles to their wide deployment. In this study, the effect of the compressing molding temperature on the VOCs and odors released by the flax/PP nonwoven composites was examined by heating nonwoven preforms in a temperature range up to 240 °C. During the hot-pressing process, real-time and in situ monitoring of the composite materials’ core temperature has been carried out using a thermocouples sensor. A chemical approach based on headspace solid-phase microextraction (HS-SPME) coupled with gas chromatography—mass spectrometry (GC-MS) was used for the VOCs analysis. The olfactory approach is based on the odor intensity scale rated by expert panelists trained in olfaction. The results demonstrate marked changes in the VOCs composition with temperature, thus making it possible to understand the changes in the NFCs odor intensity. The results allow for optimizing the molding temperature to obtain less odorous NFC materials.