We propose and demonstrate a scheme to measure the distribution of temperature along an optical fiber based on pseudo-random sequence modulation. In our experimental work, current modulation with a pseudo-random bit sequence (PRBS) is applied to a laser diode that serves as the Brillouin pump light and reference light. Because of the independence of the spatial resolution on the PRBS length, the measurement range can be extended while maintaining high spatial resolution using a long PRBS length. Temperature-induced changes in a Brillouin frequency shift of 250 m fiber sections are clearly observed with 54 cm spatial resolution by this method.