Estimating the temperature distribution within Li-ion batteries during operation is critical for safety and control purposes. Although existing control-oriented thermal models - such as thermal equivalent circuits (TEC) - are computationally efficient, they only predict average temperatures, and are unable to predict the spatially resolved temperature distribution throughout the cell. We present a low-order 2D thermal model of a cylindrical battery based on a Chebyshev spectral-Galerkin (SG) method, capable of predicting the full temperature distribution with a similar efficiency to a TEC. The model accounts for transient heat generation, anisotropic heat conduction, and non-homogeneous convection boundary conditions. The accuracy of the model is validated through comparison with finite element simulations, which show that the 2-D temperature field (r, z) of a large format (64 mm diameter) cell can be accurately modelled with as few as 4 states. Furthermore, the performance of the model for a range of Biot numbers is investigated via frequency analysis. For larger cells or highly transient thermal dynamics, the model order can be increased for improved accuracy. The incorporation of this model in a state estimation scheme with experimental validation against thermocouple measurements is presented in the companion contribution (Part II).