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The probability density function of accretion disc luminosity fluctuations at high observed energies (i.e., energies larger than the peak temperature scale of the disc) is derived, under the assumption that the temperature fluctuations are log-normally distributed. Thin disc theory is used throughout. While log-normal temperature fluctuations would imply that the disc's bolometric luminosity is also log-normal, the observed Wien-like luminosity behaves very differently. For example, in contrast to a log-normal distribution, the standard deviation of the derived distribution is not linearly proportional to its mean. This means that these systems do not follow a linear rms-flux relationship. Instead they exhibit very high intrinsic variance, and undergo what amounts to a phase transition, in which the mode of the distribution (in the statistical sense) ceases to exist, even for physically reasonable values of the underlying temperature variance. The moments of this distribution are derived using asymptotic expansion techniques. A result that is important for interpreting observations is that the theory predicts that the fractional variability of these disc systems should increase as the observed frequency is increased. The derived distribution will be of practical utility in quantitatively understanding the variability of disc systems observed at energies above their peak temperature scale, including X-ray observations of tidal disruption events.