In 2010, Basor, Chen and Ehrhardt [J. Phys. A 43 (2010), 015204 (25 pp)] studied the (monic) time-dependent Jacobi polynomials. They proved that the diagonal recurrence coefficient α(t) satisfies a particular Painlevé V equation and the sub-leading coefficient p(n, t) satisfies the Jimbo-Miwa-Okamoto σ-form of Painlevé V under suitable transformations. In the end they made some conjectures about the large n asymptotics of the associated Hankel determinant. In this note we will derive the large n asymptotics of the Hankel determinant, together with the recurrence coefficients, the sub-leading coefficient and the square of L-norm of the time-dependent Jacobi polynomials. We will also show the relation between our problem and Heun’s differential equations.