Lithium ion batteries should always be prevented from overheating and, hence, thermal monitoring is indispensable. Since only the surface temperature of the battery can be measured, a thermal model is needed to estimate the core temperature of the battery, which can be higher and more critical. In this paper, an online parameter identification scheme is designed for a cylindrical lithium ion battery. An adaptive observer of the core temperature is then designed based on the online parameterization methodology and the surface temperature measurement. A battery thermal model with constant internal resistance is explored first. The identification algorithm and the adaptive observer is validated with experiments on a 2.3Ah 26650 lithium iron phosphate/graphite battery. The methodology is later extended to address temperature-dependent internal resistance with nonuniform forgetting factors. The ability of the methodology to track the long-term variation of the internal resistance is beneficial for battery health monitoring.