This study reports on the biochemical characterization as well as the kinetic and thermodynamic study of Aspergillus tamarii URM4634 β‐fructofuranosidase (FFase) with transfructosylating activity. Conditions for FFase activity were optimized by means of a central composite rotational design using pH and temperature as the independent variables, while residual activity tests carried out in the temperature range of 45–65°C enabled us to investigate FFase thermostability and estimate the kinetic and thermodynamic parameters of enzyme denaturation. Optimal conditions for sucrose hydrolysis and fructosyl transfer catalyzed by crude FFase were 50°C, and pH 6.0 and 7.4, respectively. The thermodynamic properties of irreversible enzyme inactivation were found to be activation energy of 293.1 kJ mol−1, and activation enthalpy, entropy, and Gibbs free energy in the ranges 290.3–290.4 kJ mol−1, 568.7–571.0 J mol−1 K−1, and 97.9–108.8 kJ mol−1, respectively. The results obtained in this study point out satisfactory enzyme activity and thermostability at temperatures commonly used for industrial fructo‐oligosaccharide (FOS) synthesis; therefore, this novel FFase appears to be a promising biocatalyst with great potential for long‐term FOS synthesis and invert sugar production. To the best of our knowledge, this is the first report on kinetic and thermodynamic parameters of an A. tamarii FFase.