In recent years, natural deep eutectic solvents (NADESs) have gained increasing attention as promising nontoxic solvents for biotechnological applications, due to their compatibility with enzymes and ability to enhance their activity. Betaine-based NADESs at a concentration of 25 wt % in a buffered aqueous solution were used as media to inhibit thermal inactivation of POXA1b laccase and its five variants when incubated at 70 and 90 °C. All the tested laccases showed higher residual activity when incubated in NADES solutions, with a further enhancement achieved also for the most thermostable variant. Furthermore, the residual activity of laccases in the presence of NADESs showed a clear advantage over the use of NADESs’ individual components. Molecular docking simulations were performed to understand the role of NADESs in the stabilization of laccases toward thermal inactivation, evaluating the interaction between each enzyme and NADESs’ individual components. A correlation within the binding energies between laccases and NADES components and the stabilization of the enzymes was demonstrated. These findings establish the possibility of preincubating enzymes in NADESs as a facile and cost-effective solution to inhibit thermal inactivation of enzymes when exposed to high temperatures. This computer-aided approach can assist the tailoring of NADES composition for every enzyme of interest.