The Cryogenic Rare Event Search with Superconducting Thermometers (CRESST) experiment employs scintillating crystals at extremely low temperatures ($\mathcal{O}(10 \, \text{mK})$) to search for nuclear recoils from hypothetical dark matter (DM) particles. CRESST has achieved thresholds below 100 eV with a wide range of target materials including CaWO$_4$, LiAlO$_2$, Al$_2$O$_3$, and Si. However, at these energies, the ability to discriminate between potential DM signals and electromagnetic background is insufficient. A detailed Geant4-based electromagnetic background model was developed for CRESST and is being continuously adapted to CRESST's current inventory of detector modules. We use a high-dimensional Bayesian likelihood fit of spectral templates to the measured spectrum to infer activities of various background sources. A template for the calibration source used to calculate the energy scale will be included in the likelihood fit. We present the status of CRESST's background model, and results from the simulation of the energy calibration. Our future plans of improving the background model are also discussed.