  We present a high spatial resolution map of the columnar electron temperature
(Tc) of a region to the south west of the Trapezium in the Orion Nebula. This
map was derived from Hubble Space Telescope images that isolated the primary
lines of HI for determination of the local extinction and of the OIII lines for
determination of Tc. Although there is no statistically significant variation
of Tc with distance from the dominant ionizing star theta1-Ori-C, we find small
scale variations in the plane of the sky down to a few arcseconds that are
compatible with the variations inferred from comparing the value of Te derived
from forbidden and recombination lines, commonly known as the t^2 problem. We
present other evidence for fine scale variations in conditions in the nebula,
these being variations in the surface brightness of the the nebula,
fluctuations in radial velocities, and ionization changes. From our Tc map and
other considerations we estimate that t^2=0.028 +-0.006 for the Orion nebula.
Shadowed regions behind clumps close to the ionization front can make a
significant contribution to the observed temperature fluctuations, but they
cannot account for the t^2 values inferred from several methods of temperature
determination. It is shown that an anomalous broadening of nebular emission
lines appears to have the same sense of correlation as the temperature
anomalies, although a causal link is not obvious.
