Lithium-ion batteries are extensively employed as primary energy storage devices in engineering applications due to their high energy density, power output, and durability. Accurate estimation of the internal temperature field is crucial to ensure performance and thermal safety, particularly considering the thermal gradient between the core and the surface. However, conventional numerical simulations are computationally expensive, limiting the real-time prediction and repeated evaluation of various operating conditions. Although deep learning-based models have been introduced to reduce computational costs, most are focusing on prediction at specific monitoring points rather than the full temperature field. In addition, purely data-driven models typically require excessive data and may fail to guarantee physical consistency. In this work, we propose a Physics-Informed Deep Operator Network to efficiently predict the two-dimensional cross-sectional temperature distribution of cylindrical lithium-ion batteries. The proposed framework simultaneously incorporates time-dependent heat generation profiles arising from charge-discharge cycles and time-independent cooling parameters as input operators. The model captures the heterogeneous thermal properties of the inner electrochemical assembly and the outer cell casing, ensuring continuous heat conduction and physical consistency across the distinct material interfaces. Additionally, spatial and temporal characteristics are distinctively processed to effectively capture complex spatiotemporal dynamics. Consequently, the model exhibits robust performance in accurately capturing the transient evolution of temperature field under dynamic heat generation rates and varying cooling conditions. By integrating simulation data with governing physical equations, the model alleviates the data dependency and physical inconsistency, resulting in improved predictive accuracy and robustness. Overall, the proposed model provides a promising framework for battery thermal analysis across various operating conditions and can be extended to multiple applications, including battery design optimization, thermal safety assessment, and the development of cooling strategies.