  We present a parameterization for the eddy diffusion profile of gas giant
exoplanets based on physical phenomena and we explore how the parameterized
eddy profile impacts the chemical composition, the thermal structure, the haze
microphysics, and the transit spectra of 8 hot-Jupiters. Our eddy
parameterization depends on the planetary intrinsic temperature (T$_{int}$ ),
we thus evaluate how the increase of this parameter to values higher than those
typically used ($\sim$100K) impacts the atmospheric structure and composition.
Our investigation demonstrates that despite the strong impact of T$_{int}$ on
the chemical composition of the deep atmosphere, the upper atmosphere is not
affected for T$_{eq}$ $>$ 1300 K owing to high altitude quench levels at these
conditions. Below this threshold, however, the larger atmospheric temperatures
produced by increasing T$_{int}$ affect the quenched chemical composition. Our
parameterization depends on two parameters, the eddy magnitude at the
radiative-convective boundary (K$_0$) and the corresponding magnitude at the
homopause (K$_{top}$). We demonstrate that, when using common K$_0$ and
K$_{top}$ values among most of the different planet cases studied, we derive
transit spectra consistent with Hubble Space Telescope observations. Moreover,
our simulations show that increasing the eddy profile enhances the
photochemical production of haze particles and reduces their average radius,
thus providing a steeper UV-Visible slope. Finally, we demonstrate for WASP-39b
that the James Webb Space Telescope observations provide improved constraints
for the hazes and clouds and we show that both components seem necessary to
interpret the combined transit spectrum from HST and JWST observations.
