The thermal stability of bovine serum albumin (BSA) in Tris buffer, as well as the effect of sinapic acid (SA) on protein conformation were investigated via calorimetric (differential scanning microcalorimetry—μDSC), spectroscopic (dynamic light scattering—DLS; circular dichroism—CD), and molecular docking approaches. μDSC data revealed both the denaturation (endotherm) and aggregation (exotherm) of the protein, demonstrating the dual effect of SA on protein thermal stability. With an increase in ligand concentration, (i) protein denaturation shifts to a higher temperature (indicating native form stabilization), while (ii) the aggregation process shifts to a lower temperature (indicating enhanced reactivity of the denatured form). The stabilization effect of SA on the native structure of the protein was supported by CD results. High temperature (338 K) incubation induced protein unfolding and aggregation, and increasing the concentration of SA altered the size distribution of the protein population, as DLS measurements demonstrated. Complementary information offered by molecular docking allowed for the assessment of the ligand binding within the Sudlow’s site I of the protein. The deeper insight into the SA–BSA interaction offered by the present study may serve in the clarification of ligand pharmacokinetics and pharmacodynamics, thus opening paths for future research and therapeutic applications.