There is currently no theory for the rate of tropical cyclone (TC) formation given a particular climate, so our understanding of the relationship between TC frequency and large‐scale environmental factors is largely empirical. Here, we explore the sensitivity of TC formation and intensification rates to climate warming in a series of highly idealized cloud‐permitting simulations, in which TCs form spontaneously from a base state of rest on an f‐plane. The simulations reveal a nonmonotonic relationship between the time taken for a TC precursor disturbance (a “seed”) to form and the prescribed sea surface temperature (SST), with moderately long seed emergence times at both ends of the SST range tested (292 and 304 K) and a shorter seed emergence time at the middle value of SST (298 K). Genesis potential indices (GPIs) exhibit a different response to warming: either a monotonic increase if the potential intensity and midtropospheric relative humidity are used or relatively little sensitivity if the saturation deficit is used as the humidity variable. The sensitivity of elapsed time between a TC seed disturbance and TC genesis to surface warming is, however, generally well captured by GPIs, especially those that depend on the saturation deficit. The maximum intensification rate of TCs increases strongly with warming, particularly during the second half of the intensification process. Notably, storms intensify much more rapidly with increasing temperature than is predicted by extant theory based on potential intensity, suggesting that TCs in a warmer climate may intensify even more rapidly than recent studies suggest.