  In this paper, within the framework of modified gravity involving a conformal
scalar field, we investigate the Joule-Thomson expansion of the FRW universe to
identify cooling and heating regions. Notably, we observe that the
Joule-Thomson coefficient, denoted as $\mu$, diverges at $R_A=\sqrt{-2\alpha}$
when $\alpha<0$, aligning with the thermodynamic singularity of the FRW
universe. Additionally, we determine the inversion temperature and inversion
pressure for the FRW universe, and illustrate the characteristics of inversion
curves and isenthalpic curves in the $T$-$P$ plane. We compare these findings
with results obtained under Einstein gravity, discussing the influence of the
modification term on the cooling and heating properties of the FRW universe.
This work contributes significantly to a deeper understanding of the formation
of cooling and heating regions within the FRW universe, thereby advancing our
comprehension of the physical mechanisms that govern the expansion of our
universe.
