Recent studies have found that the spectral evolution of pulses within gamma-ray bursts (GRBs) is consistent with simple radiative cooling. Perhaps more interesting was a report that some bursts may have a single cooling rate for the multiple pulses that occur within it. We determine the probability that the observed “cooling rate invariance” is purely coincidental by sampling values from the observed distribution of cooling rates. We find a 0.1–26&percent; probability that we would randomly observe a similar degree of invariance based on a variety of pulse selection methods and pulse comparison statistics. This probability is sufficiently high to warrant skepticism of any intrinsic invariance in the cooling rate. ©1998 American Institute of Physics.