We report soft X-ray spectra (4-18 nm) produced by the interaction of 25-100-fs laser pulses at an intensity of up to 7 X 10(16) W/cm(2) with a cryogenically cooled Ar gas jet. New spectral lines from Ar8+, Ar9+, and Ar10+ charge states appeared with decreasing preexpansion gas temperature. A nonlinear increase of X-ray line emission from Ar7+, Ar8+, and Ar9+ was observed with cooling, which saturated below a certain temperature. The drastic change in the spectrum is attributed to efficient collisional heating and collisional ionization of growing, small- to medium-sized (10(2)-10(3) atoms) Ar clusters from the cooled jet. When the laser pulse was extended from 25 to 100 fs we observed considerably stronger emission on lines from high charge states, such as Ar8+, Ar9+, and Ar10+, which suggests that the resonance absorption condition could be reached for the 100-fs pulse.