The temperature-dependence coefficient of Brillouin frequency shift (BFS) in perfluorinated graded-index polymer optical fibers is known to change drastically, because of the glass transition, at a certain critical temperature (Tc), above which the BFS becomes more sensitive to temperature. In this paper, we demonstrate that the Tc value can be adjusted by varying the dopant concentration, which is originally used to form the graded-index profile in the core region. Furthermore, we show that the temperature sensitivity of the BFS is enhanced in the presence of dopant probably because the temperature sensitivity of Young's modulus is increased. The results indicate a big potential of the temperature sensors based on Brillouin scattering with an extremely high sensitivity in a specific desired temperature range.