Starting with a hypothetical geostrophic zonal current in an unbounded ocean, the investigation points out the response of this simple system to a thermal forcing, applied to the free surface and consistent with the maintenance of the geostrophic balance. The main result is the formation of a meridional component of the current, according to the Sverdrup relation, such that the full velocity vector rotates clockwise for heating and anticlockwise for cooling to adjust eventually in the initial zonal direction for large depths.