In this work, we present a numerical study of the thermal insulation of a heated two dimensional cavity limited on its superior part by a horizontal plane air jet. The lower horizontal wall is isothermal, while the two vertical walls are adiabatics. A finite difference method based on the stream function-vorticity formulation is developed to solve the dimensionless Navier-Stokes and energy equations resulting from some assumptions. The results allowed us to point out two flow configurations: if natural convection prevails, the hot jet issuing from the nozzle diffuses upwards, and consequently, the cavity cannot be insulated correctly. However, the use of an aspiration zone can then improve the insulation. When forced convection predominates, the hydrodynamic barrier is conserved, and the enclosure is also thermally well confined.