Possible rapid cooling of a higher temperature plasma is investigated in a gas-contact cooling method in which the effect of finite time for mixing the plasma and the contact gas is considered. The calculation has shown that cooling under these conditions is much more rapid than that achieved by radiative loss cooling and that the gain per unit length of the He II 164 nm line is approximately 2 cm-1 for the laser oscillation under optimum conditions. The possibility of realising a laser at a shorter wavelength in a plasma with higher charge number Z is also discussed.