A warm Maxwellian plasma can stabilize velocity‐space instabilities which might otherwise occur in a hot non‐Maxwellian plasma with which it coexists. The relative densities and temperatures of the two species required for stabilization of resonant (&ohgr; ≈ l&OHgr;i, the ion gyroharmonics) loss‐cone modes in a mirror‐confined hot‐ion plasma are evaluated for a model plasma whose density is spatially uniform but whose velocity‐space distribution function simulates the loss‐cone effect of mirror confinement. Marginal stability boundaries are given and compared with several simple but inexact criteria. The dominant features of the stability boundaries are explained on the basis of cutoff of propagation of the unstable waves. Temporal growth rates of the absolutely unstable modes are found to decrease significantly with increasing warm‐plasma density. The resulting transition from absolute to convective growth is demonstrated for the first two gyroharmonics.