Soft-x-ray emission from a cryogenically cooled Ne jet irradiated; by intense, 25-fs laser pulses was measured. The Ne spectrum started to drastically change in emitting ions from Ne5+ to Ne7+ below the preexpansion temperature of - 120 degrees C. The significant change in the spectrum is attributed to the collisional heating of small-sized Ne clusters formed in the cooled jet. The increase of the laser pulse length from 25 fs to 100 fs resulted in further increase of x-ray emission from Ne7+ states.