Observations and numerical simulators of tropical cyclones show that evaporation from the sea surface is essential to the development of reasonably intense storms. On the other hand, the CISK hypothesis, in the form originally advanced by Charney and Eliassen, holds that initial development results from the organized release of preexisting conditional instability. In this series of papers, we explore the relative importance of ambient conditional instability and air-sea latent and sensible heat transfer in both the development and maintenance of tropical cyclones using highly idealized models. In particular, we advance the hypothesis that the intensification and maintenance of tropical cyclones depend exclusively on self-induced heat transfer from the ocean. In this sense, these storms may be regarded as resulting from a finite amplitude air-sea interaction instability rather than from a linear instability involving ambient potential buoyancy. In the present paper, we attempt to show that reasonably intense cyclones may be maintained in a steady state without conditional instability of ambient air. In Part II we will demonstrate that weak but finite-amplitude axisymmetric disturbances may intensify in a conditionally neutral environment.