  The purpose of this paper is twofold. Firstly, we conduct an in-depth
analysis of mathematical modeling concerning thermal-mechanical curved beams,
by taking into consideration three primary forces widely accepted in the
literature: axial load, shear force, and bending moment. Additionally, we
examine their appropriate thermal couplings, shedding light on the intricate
interplay between stress-strain relationships and temperature variations. This
analysis is situated within the well-recognized context of the Bresse governing
model for arched beams. Secondly, drawing upon distinguished constitutive laws
for heat flux of conduction, we compile a comprehensive list of thermoelastic
curved beam systems in various scenarios. We introduce new categories of
problems that exhibit specific features from the thermal point of view.
