We investigate the temperature-dependences of the Brillouin frequency shift in a tellurite glass fiber and a bismuth-oxide highly-nonlinear fiber using a Brillouin optical correlation-domain reflectometry system for sensing applications. Negative dependences of -1.14 and -0.88 MHz/K are demonstrated, respectively, in contrast to the positive dependence of +1.18 MHz/K in a standard silica fiber.