This paper presents a 2-D numerical study to investigate the fluid flow behavior and cooling characteristics caused by injecting tiny droplets into the sweeping air jet through a fluidic oscillator. An unsteady Reynolds-averaged Navier-Stokes simulation accompanied with the k-ω SST turbulence model is used in this study. The movement and evaporation of the mist are simulated by using the discrete phase model. The study has been conducted for a target wall with a constant heat flux of 3,000 W/m2, jet-to-wall distance of 4, ReD=2,500, and a mist /air mass ratio of 5% with a droplet size of 5 microns. A comparison between the cooling performance of steady and sweeping jets is presented for two impingement schemes. The approach of using a slip upper wall boundary condition as an alternative of the unconfined impingement scheme is investigated as well. The results show that adding mist provided a temperature reduction of 5-10% on the target wall in all cases when compared to the air cases. The liquid droplet coalescence phenomenon prevails in the sweeping jet case. For the confined impingement, both mist jets provided the similar average temperature reduction. However, the steady mist jet introduced a 58% more target wall shear compared to the sweeping mist jet. For the unconfined impingement, the steady mist jet achieved a better average cooling performance compared to that of the sweeping mist jet. However, the steady mist jet introduced a 72% more target wall shear.