  Temperature profiles of the hot galaxy cluster intracluster medium (ICM) have
a complex non-linear structure that traditional parametric modelling may fail
to fully approximate. For this study, we made use of neural networks, for the
first time, to construct a data-driven non-parametric model of ICM temperature
profiles. A new deconvolution algorithm was then introduced to uncover the true
(3D) temperature profiles from the observed projected (2D) temperature
profiles. An auto-encoder-inspired neural network was first trained by learning
a non-linear interpolatory scheme to build the underlying model of 3D
temperature profiles in the radial range of [0.02-2] R$_{500}$, using a sparse
set of hydrodynamical simulations from the THREE HUNDRED PROJECT. A
deconvolution algorithm using a learning-based regularisation scheme was then
developed. The model was tested using high and low resolution input temperature
profiles, such as those expected from simulations and observations,
respectively. We find that the proposed deconvolution and deprojection
algorithm is robust with respect to the quality of the data, the morphology of
the cluster, and the deprojection scheme used. The algorithm can recover
unbiased 3D radial temperature profiles with a precision of around 5\% over
most of the fitting range. We apply the method to the first sample of
temperature profiles obtained with XMM{\it -Newton} for the CHEX-MATE project
and compared it to parametric deprojection and deconvolution techniques. Our
work sets the stage for future studies that focus on the deconvolution of the
thermal profiles (temperature, density, pressure) of the ICM and the dark
matter profiles in galaxy clusters, using deep learning techniques in
conjunction with X-ray, Sunyaev Zel'Dovich (SZ) and optical datasets.
