An analysis of the response of the tropical atmosphere to isolated equatorially asymmetric heating is performed using the Gill model. General solutions of the Gill model are calculated, and the equatorially asymmetric atmospheric response is examined in detail within the general solutions. Heating strength, location, and extent all have some influence on the atmospheric response. When the center of heating moves northward, the cyclone in the Northern Hemisphere is strengthened and moves northward; at the same time, equatorial convergence weakens and cross-equatorial flow is enhanced. When heating strength increases (decreases), the atmospheric response forced by the heating is enhanced (weakened), however, the atmospheric pattern does not vary. When the heating extent increases, the cyclonic strength and extent are enhanced, the cyclone is displaced westward, and cross-equatorial flow is enhanced. The above theoretical conclusions are applied to study of the influence of SST on the onset of monsoons in the Bay of Bengal. When the meridional warmest SST axis (WSSTA) is located at the equator, the Gill pattern appears on either side of the equator; however, when the WSSTA moves northward, cyclonic circulation disappears and cross-equatorial flow is induced south of the WSSTA. This effect represents the response of mixed Rossby-gravity waves to external heat forcing. This work shows the utility of the above analytic approach, and also explains the dynamics responsible for summer monsoon onset in the Bay of Bengal.