The thermal behavior of a fluid-cooled battery can be modeled using computational fluid dynamics (CFD). Depending on the size and complexity of the battery module and the available computing hardware, the simulation can take days or weeks to run. This work introduces a reduced-order model that combines proper orthogonal decomposition, capturing the variation of the temperature field in the spatial domain, and linear time-invariant system techniques exploiting the linear relationship between the resulting proper orthogonal decomposition coefficients and the uniform heat source considered here as the input to the system. After completing an initial CFD run to establish the reduction, the reduced-order model runs much faster than the CFD model. This work will focus on thermal modeling of a single prismatic battery cell with one adjacent cooling channel. The extension to the multiple input multiple output case such as a battery module will be discussed in another paper.