The mineralogical composition of dust contains important information regarding the origin and processing of the dust and the physical, chemical, and evolutionary properties of the astrophysical environment where the dust is found. In the literature, the composition of cosmic dust is usually inferred by fitting the observed infrared (IR) emission spectrum with a sum of emission spectra calculated from various individual grain species of different sizes but assuming a single, identical temperature for them. However, we show in this work that these grains of different compositions and/or different sizes, while in thermal equilibrium with the radiation field to which the grains are exposed, achieve different temperatures. The effects of dust temperature on dust compositional studies are demonstrated by showing that the IR emission spectrum calculated from a mixture of grains emitting at different temperatures differs substantially from that of the same grain mixture but with a single, identical temperature. Therefore, the need for obtaining realistic temperatures from realistic cosmic dust analogs is a key to properly interpreting the observational IR emission spectra, e.g., the rich set of data that the Spitzer Space Telescope has been collecting.