The maximum reduction in the average temperature ⟨T⟩z=b−1∫0bd z Tof a slab of thicknessbthat can be obtained in both a short period of time, typically[inverted lazy s]1 sec,and a long period of time (steady‐state approached) without causing material failure is calculated. The slab is originally at a constant temperature, and ⟨T⟩zis the temperature that determines the optical properties of a normally illuminated slab. The results indicate that Ge28Sb12Se60glass can be cooled rapidly enough for use in laser systems at relatively high power levels (several hundred W/cm2) in the pulse mode of operation discussed previously, in contrast to previous beliefs. There is a time constant &tgr;sfor the nonexponential approach of the surface temperatureTsof a semi‐infinite medium to the temperatureTcof the coolant. Consider the thermally thin‐disk case of&tgr;b≪&tgr;s, where &tgr;bis time required for heat to diffuse across the thicknessb, roughly speaking. The value of ⟨T⟩zthen approachesTcexponentially with a time constant &tgr;c, which is much smaller than &tgr;s. For the thermally thick‐disk case of&tgr;s≪&tgr;b,⟨T⟩z[inverted lazy s](t/&tgr;c)Tcfort≪&tgr;s; ⟨T⟩z≃(t/&tgr;b)1/2Tcfor&tgr;s≪t≪&tgr;b; and ⟨T⟩z≃Tcfort≫&tgr;b.The solution to the heat‐flow equation forTis known in simple closed form for the case of a semi‐infinite medium. The result is quite accurate for finite disks, both thermally thick and thin, whent≪&tgr;bis satisfied. For this case oft≪&tgr;b, the maximum value of the magnitude of the stress component |&sgr;xx|(=|&sgr;yy|) is determined by the surface temperatureTsonly. For a given temperature difference across the disk, the maximum value of |&sgr;xx| is less for the case oft≥&tgr;bthan for the case oft≪&tgr;b. Two examples, GaAs and Ge28Sb12Se60glass, are considered.