There is currently no theory for the rate of tropical cyclone (TC) formation given a particular climate, and so our understanding of the relationship between TC frequency and large-scale environmental factors is largely empirical (i.e., genesis potential indices).  Here, we explore the sensitivity of TC genesis to sea surface temperature (SST) in a series of highly-idealized cloud-permitting simulations, in which TCs evolve from a base state of rest on an f-plane.  The simulations reveal a non-monotonic relationship between the time it takes for TCs to form and the prescribed SST, with moderately long spin-up times at both ends of the SST spectrum tested (292 K and 304 K), and a relatively fast evolution to genesis at the middle value of SST (298 K).  In contrast, genesis potential indices diagnosed from the simulations display a monotonic increase with increasing SST, which is consistent with projections from global climate models.  Our results suggest that the combination of sufficiently high values of near-surface gustiness (which decreases with warming) and mid-tropospheric relative humidity (which increases with warming) produce an optimal state for TC formation.  The implications for TC frequency projections in global climate models will also be discussed.