The correlation between the temporal and spatial variations of the elastic constant and temperature change was examined for a light guide plate (LGP) adopted in the edge-lit light-emitting-diode backlight for mobile applications, using the micro- Brillouin light scattering method. The velocity of sound and the elastic constant $C_{11}$ of an LGP made from bisphenol-A polycarbonate (PC) were investigated as functions of temperature, time, and position on the LGP. The temporal variation of $C_{11}$ exhibited an exponential decay, while the spatial variation of $C_{11}$ reflected the temperature distribution on the LGP. The glass transition temperature of the PC LGP was found to be located at $155^{circ}C$. The result showed that systematic transformation between the elastic property and the temperature is possible and that the temperature distribution on the bulk LGP can be accurately probed via the present experiment method, without using any special temperature measurement equipment.