Friction stir-spot welding (FSSW) as a solid-state joining process for local welding offers a number of benefits for applications in the automotive, aerospace, and marine industries. In these industries, and from an economic point of view, producing spot welds at a low rotating speed and in a short time is critical for saving energy and enhancing productivity. This investigation helped fill a knowledge gap in the literature about FSSW of 4 mm similar lap joints of AA5052-H32 sheet materials, in which welding takes place over a short time period with a slow tool rotation speed. Consequently, the purpose of this work was to investigate the feasibility of FSSW 2 mm thick AA5052-H32 aluminum alloy sheets to produce 4 mm thick similar spot lap joints at various low dwell times of 1, 2, and 3 s and a constant relatively low tool rotation speed of 500 rpm. The introduced heat input for the friction stir-spot welded (FSSWed) lap joints was calculated based on the applied processing parameters. Joint appearance, cross-section macrostructures, and microstructure features of all the spot welds were evaluated. The mechanical properties (hardness contour maps and maximum tensile shear loads) were also examined. The results show that joining 2 mm sheet thickness AA5052-H32 at a low heat input in defect-free similar lap joints could be successfully achieved. The stir zone (SZ) region became wider as the dwell time increased from 1 to 3 s. The hardness value of the SZ was higher than that attained by the AA5052-H32 base material (BM) for all applied dwell times. Especially at 2 s, the hardness of the SZ was approximately 48% higher than that of the BM. This increase in hardness may be attributed to the high grain refinement of the new dynamically recrystallized grain (4 µm) in the SZ compared to the cold-rolled BM grain size (40 µm). Among the tried FSSW process variables, the dwell time of 2 s at a rotation rate of 500 rpm also produced the maximum tensile shear load of 4330 N. Finally, the locations and features of the fracture surfaces of the FSSWed joints were examined using a scanning electron microscope (SEM) and the obtained results were discussed.