  We present full-orbit phase curve observations of the eccentric ($e\sim
0.08$) transiting hot Jupiter WASP-14b obtained in the 3.6 and 4.5 $\mu$m bands
using the \textit{Spitzer Space Telescope}. We use two different methods for
removing the intrapixel sensitivity effect and compare their efficacy in
decoupling the instrumental noise. Our measured secondary eclipse depths of
$0.1882\%\pm 0.0048\%$ and $0.2247\%\pm 0.0086\%$ at 3.6 and 4.5 $\mu$m,
respectively, are both consistent with a blackbody temperature of $2402\pm 35$
K. We place a $2\sigma$ upper limit on the nightside flux at 3.6 $\mu$m and
find it to be $9\%\pm 1\%$ of the dayside flux, corresponding to a brightness
temperature of 1079 K. At 4.5 $\mu$m, the minimum planet flux is $30\%\pm 5\%$
of the maximum flux, corresponding to a brightness temperature of $1380\pm 65$
K. We compare our measured phase curves to the predictions of one-dimensional
radiative transfer and three-dimensional general circulation models. We find
that WASP-14b's measured dayside emission is consistent with a model atmosphere
with equilibrium chemistry and a moderate temperature inversion. These same
models tend to over-predict the nightside emission at 3.6 $\mu$m, while
under-predicting the nightside emission at 4.5 $\mu$m. We propose that this
discrepancy might be explained by an enhanced global C/O ratio. In addition, we
find that the phase curves of WASP-14b ($7.8 M_{\mathrm{Jup}}$) are consistent
with a much lower albedo than those of other Jovian mass planets with thermal
phase curve measurements, suggesting that it may be emitting detectable heat
from the deep atmosphere or interior processes.
