  [Abridged] Aims. We present a large atmospheric study of 49 gas giant
exoplanets using infrared transmission photometry with Spitzer/IRAC at 3.6 and
4.5um. Methods. We uniformly analyze 70 photometric light curves of 33
transiting planets using our custom pipeline, which implements pixel level
decorrelation. We use this survey to understand how infrared photometry traces
changes in atmospheric chemical properties as a function of planetary
temperature. We compare our measurements to a grid of 1D radiative-convective
equilibrium forward atmospheric models which include disequilibrium chemistry.
We explore various strengths of vertical mixing (Kzz = 0 - 10^12 cm2/s) as well
as two chemical compositions (1x and 30x solar). Results. We find that, on
average, Spitzer probes a difference of 0.5 atmospheric scale heights between
3.6 and 4.5um, which is measured at 7.5sigma level of significance. We find
that the coolest planets show a lack of methane compared to expectations, which
has also been reported by previous studies of individual objects. We show that
the sample of coolest planets rule out 1x solar composition with >3sigma
confidence while supporting low vertical mixing (Kzz = 10^8 cm2/s). On the
other hand, we find that the hot planets are best explained by models with 1x
solar metallicity and high vertical mixing (Kzz = 10^12 cm2/s). We interpret
this as the lofting of CH4 to the upper atmospheric layers. Changing the
interior temperature changes the expectation for equilibrium chemistry in deep
layers, hence the expectation of disequilibrium chemistry higher up. We also
find a significant scatter in the transmission signatures of the mid-temperate
and ultra-hot planets, likely due to increased atmospheric diversity, without
the need to invoke higher metallicities. Additionally, we compare Spitzer
transmission with emission for the same planets and find no evidence for
correlation.
