This paper concerns with properties of a thermal convection in a stably stratified Boussinesq fluid caused by partial heating or cooling of the lower boundary. For infinitesimal heating (cooling) the convective motion can be described by a linear theory. Introducing a suitable scaling, it is shown that the convection is controlled mainly by a non-dimensional parameter, R=ag*l4/k* where * is the vertical temperature gradient in the basic state, l is the half-width of the heated (cooled) area and the other symbols have conventional meanings. The convective motion is confined to the "frictional depth" introduced by Stommel and Veronis (1957). For a single slab-symmetric heating (cooling) the thickness (the lowest height at which the temperature perturbation vanishes) is given by hT=3.6 R-l/6 and the maximum horizontal velocity by u*max= 0.25,*\Th\ where Pr= */k and Th is the temperature difference between the heated (cooled) area and the surrounding area. The width of the upward (downward) motion area is close to the horizontal scale of the forcing area.The convection patterns for the finite-amplitude heating (cooling) were investigated by means of laboratory and numerical experiments for |Th|**l.It was observed that increase of the thickness of the boundary layer with Th is small. As for the convection caused by heating, however, the width of the upward motion area decreases with the increase of Th until the magnitude of the upward motion becomes comparable with that of the horizontal motion. As for the convection caused by cooling, the width of the downward motion area increases with |T h|, but the essential features of the convection pattern are similar to those for the infinitesimal cooling.These results are compared with available data of the convection due to the urban heat island effect.