Lithium-ion (Li-ion) batteries and issues related to their thermal management and safety have been attracting extensive research interests. In this work, based on a recent thermal chemistry model, the phenomena of thermal runaway induced by a transient internal heat source are computationally investigated using a three-dimensional (3D) model built in COMSOL Multiphysics 5.3. Incorporating the anisotropic heat conductivity and typical thermal chemical parameters available from literature, temperature evolution subject to both heat transfer from an internal source and the activated internal chemical reactions is simulated in detail. This paper focuses on the critical runaway behavior with a delay time around 10s. Parametric studies are conducted to identify the effects of the heat source intensity, duration, geometry, as well as their critical values required to trigger thermal runaway. The characteristics of different concentrations and heat release from each chemical reaction in the scenario of thermal runaway are discussed. Based on the current kinetic model, the simulation results further suggest that the concentration of negative-electrolyte is closely related to the occurrence of thermal runaway. This study provides useful guidance on the simulation and control of thermal runaway of battery systems.