We investigate the steady dynamical response of the atmosphere on the equatorial β-plane to a steady, localized, mid-tropospheric heating source at the equator. Expanding Gill (1980)’s seminal work, we vary the latitudinal and longitudinal scales of the diabatic heating pattern while keeping its total amount fixed. We focus on characteristics of the response which would be particularly important if the circulation interacted with the hydrologic and energy cycles: the overturning circulation and the low-level wind. In the limit of very small scale in either the longitudinal or latitudinal direction, the vertical energy transport balances the diabatic heating and this sets the intensity of the overturning circulation. In this limit, a fast low-level westerly jet is located around the center of diabatic heating. With increasing longitudinal or latitudinal scale of the diabatic heating, the intensity of the overturning circulation decreases and the low-level westerly jet decreases in maximum velocity and spatial extent relative to the spatial extent of this heating. The associated low-level eastward mass transport decreases only with increasing longitudinal scale. These results suggest that moisture-convergence feedbacks will favor small-scale equatorial convective disturbances while surface-heat-flux feedbacks would favor small-scale disturbances in mean westerlies and large-scale disturbances in mean easterlies. Part~II investigates the case of off-equatorial heating.