In the present study, laminar pulsating flow over a backward-facing step in the presence of a square obstacle placed behind the step is numerically studied to control the heat transfer and fluid flow. The working fluid is air with a Prandtl number of 0.71 and the Reynolds number is varied from 10 and 200. The study is performed for three different vertical positions of the square obstacle and different forcing frequencies at the inlet position. Navier–Stokes and energy equation for a 2D laminar flow are solved using a finite-volume-based commercial code. It is observed that by properly locating the square obstacle the length and intensity of the recirculation zone behind the step are considerably affected, and hence, it can be used as a passive control element for heat transfer augmentation. Enhancements in the maximum values of the Nusselt number of 228% and 197% are obtained for two different vertical locations of the obstacle. On the other hand, in the pulsating flow case at Reynolds number of 200, two locations of the square obstacle are effective for heat transfer enhancement with pulsation compared to the case without obstacle.