Betatron stochastic cooling will be built to cool hot beams in very short time on HIRFL-CSRm during its stripping injection. Here the transverse cooling is described and simulated. The cooling time and the beam distribution are obtained. The power-limited cooling system, which performance is limited by available output power, is contrasted with non-power-limited system and the upgrading is also mentioned. All these are useful for analysis of experimental data and for design of the cooling system and running, i.e., optimization of the system passband specification of accuracy of the signal's transmission, etc.