  In a high temperature regime, it was shown in Trinh--Trinh (\emph{J.\ Stat.\
Phys.}\ \textbf{185}(1), Paper No.\ 4, 15 (2021)) that the empirical
distribution of beta Jacobi ensembles converges to a limiting probability
measure which is related to Model III of associated Jacobi polynomials. In this
paper, we establish Gaussian fluctuations around the limit whose statement
involves orthogonal polynomials. For the proofs, we refine a moment method at
the process level which has been used to deal with Gaussian beta ensembles and
beta Laguerre ensembles.
