We demonstrate the use of the micro-Brillouin light scattering (micro-BLS) technique as a local temperature sensor for magnons in a Permalloy thin film and phonons in the glass substrate. A systematic shift in the frequencies of two thermally excited perpendicular standing spin wave modes as the film is uniformly heated allows us to achieve a temperature resolution better than 2.5 K. We demonstrate that the micro-BLS spectra can be used to measure the local temperatures of phonons and magnons across a thermal gradient. Such local temperature sensors are useful for investigating spin caloritronic and thermal transport phenomena in general.