  The magnitude of the temperature fluctuations (t^2) required to explain the
observed inconsistencies between metallicities inferred from recombination
lines and from forbidden lines cannot be attained by steady-state equilibrium
photoionization models. If on the other hand the nebular ionizing source was
variable, the temperature fluctuations t^2 would be significantly larger. We
investigate the time-dependent response of the nebular ionization and
temperature structure when photoionized by a periodically varying source. We
study how the asymptotic mean value, <t^2>, behaves as a function of the period
or amplitude of the source variability. We find that the temperature
fluctuations occur only in the outer section of the nebula, close to the
ionization front, within a zone corresponding to 8-20% of the ionized layer's
thickness. We conclude that the amplitude of the exciting star variations
required to achieve a <t^2> = 0.025 (as in the Orion nebula) is unacceptably
large. Source variability is therefore not a viable mechanism to explain the
observed values of t^2. We reach a similar conclusion from studies of the
temporal variability resulting from intermittent shadows behind opaque
condensations. We find that photoionized nebulae are on average less massive
but somewhat hotter in the case of cyclicly variable ionizing sources.
