  Spectroscopic eclipse observations, like those possible with the James Webb
Space Telescope, should enable 3D mapping of exoplanet daysides. However,
fully-flexible 3D planet models are overly complex for the data and
computationally infeasible for data-fitting purposes. Here, we present ThERESA,
a method to retrieve the 3D thermal structure of an exoplanet from eclipse
observations by first retrieving 2D thermal maps at each wavelength and then
placing them vertically in the atmosphere. This approach allows the 3D model to
include complex thermal structures with a manageable number of parameters,
hastening fit convergence and limiting overfitting. An analysis runs in a
matter of days. We enforce consistency of the 3D model by comparing vertical
placement of the 2D maps with their corresponding contribution functions. To
test this approach, we generated a synthetic JWST NIRISS-like observation of a
single hot-Jupiter eclipse using a global circulation model of WASP-76b and
retrieved its 3D thermal structure. We find that a model which places the 2D
maps at different depths depending on latitude and longitude is preferred over
a model with a single pressure for each 2D map, indicating that ThERESA is able
to retrieve 3D atmospheric structure from JWST observations. We successfully
recover the temperatures of the planet's dayside, the eastward shift of its
hotspot, and the thermal inversion. ThERESA is open-source and publicly
available as a tool for the community.
