  An important focus of exoplanet research is the determination of the
atmospheric temperature structure of strongly irradiated gas giant planets, or
hot Jupiters. HD 209458b is the prototypical exoplanet for atmospheric thermal
inversions, but this assertion does not take into account recently obtained
data or newer data reduction techniques. We re-examine this claim by
investigating all publicly available Spitzer Space Telescope secondary-eclipse
photometric data of HD 209458b and performing a self-consistent analysis. We
employ data reduction techniques that minimize stellar centroid variations,
apply sophisticated models to known Spitzer systematics, and account for
time-correlated noise in the data. We derive new secondary-eclipse depths of
0.119 +/- 0.007%, 0.123 +/- 0.006%, 0.134 +/- 0.035%, and 0.215 +/- 0.008% in
the 3.6, 4.5, 5.8, and 8.0 micron bandpasses, respectively. We feed these
results into a Bayesian atmospheric retrieval analysis and determine that it is
unnecessary to invoke a thermal inversion to explain our secondary-eclipse
depths. The data are well-fitted by a temperature model that decreases
monotonically between pressure levels of 1 and 0.01 bars. We conclude that
there is no evidence for a thermal inversion in the atmosphere of HD 209458b.
