There is evidence for temperature fluctuations in planetary nebulae an
d in some Galactic H II regions. If such fluctuations occur in the low
-metallicity, extragalactic H II regions used to probe the primordial
helium abundance, the derived He-4 mass fraction, Y-p, could be system
atically different from the true primordial value. For cooler, mainly
high-metallicity H II regions, the derived helium abundance may be nea
rly unchanged, but the oxygen abundance could have been seriously unde
restimated. For hotter, mainly low-metallicity H II regions, the oxyge
n abundance is likely accurate, but the helium abundance could be unde
restimated. The net effect is to tilt the Y-versus-Z relation, making
it flatter and resulting in a higher inferred Y-p. Although this effec
t could be large, there are no data that allow us to estimate the size
of the temperature fluctuations for the extragalactic H II regions. T
herefore, we have explored this effect via Monte Carlo simulations of
the data in which the abundances derived from a fiducial data set are
modified by Delta T chosen from a distribution with 0 less than or equ
al to Delta T less than or equal to Delta T-max where Delta T-max is v
aried from 500 to 4000 K. It is interesting that, although this effect
shifts the locations of the H II regions in the Y-versus-O/H plane, i
t does not introduce any significant additional dispersion.