The masonry wall initially saturated with moisture and without internal or external water sources was considered to simulate the drying of a wall after a flood. Numerical calculations using the in-house non-equilibrium heat and moisture model were performed to investigate the impact of variable drying air temperature profiles on the drying efficiency of the thermo-injection method. A drying process lasting twelve days was simulated. Based on previous studies, four drying air temperature variation strategies, i.e., jump, stepwise, periodic, and constant temperature (reference), were computed and compared. The drying air temperature profile was changed from 20°C to 60°C with heating intervals of 24 h and different characterization strategies. The jump strategy changed rapidly in a single step. Stepwise one changed by 10°C after each heating interval, and the period strategy changed from 20°C to 60°C or from 60°C to 20°C after each heating interval. Furthermore, the relative humidity of the drying air corresponded to the three seasons in Poland (i.e., winter, summer, and spring) and ranged between 70% and 90% at ambient conditions. It was found that the proposed drying strategies with variable temperature profiles can reduce energy consumption compared to the reference strategy with a constant temperature.