Aims: We investigate the variability in temperature as a function of time among a sample of coronal X-ray bright points (XBPs). Methods: We analysed a 7-h (17:00-24:00 UT) long time sequence of soft X-ray images observed almost simultaneously in two filters (Ti_poly and Al_mesh) on April 14, 2007 with X-ray telescope (XRT) onboard the Hinode mission. We identified and selected 14 XBPs for a detailed analysis. The light curves of XBPs were derived using the SolarSoft library in IDL. The temperature of XBPs was determined using the calibrated temperature response curves of the two filters by means of the intensity ratio method. Results: We find that the XBPs show a high variability in their temperature and that the average temperature ranges from 1.1 MK to 3.4 MK. The variations in temperature are often correlated with changes in average X-ray emission. It is evident from the results of time series that the XBP heating rate can be highly variable on short timescales, suggesting that it has a reconnection origin.