Krylov-based methods are an attractive alternative to traditional fixed-point iterative schemes, being much more robust and accurate when solving elliptic equations (e.g., the energy equation in the solid domain). This study assesses the performance of a Krylov-based accelerator, when used for conjugate heat transfer (CHT) simulations of an electrical battery pack. The nonlinear nature of CHT simulations (due to spatial and temporal changes in boundary conditions) necessitates the use of the non-inear form of the Krylov-based accelerator (termed NKA), which utilizes the generalized minimized residual (GMRES) method, and works by accelerating an existing fixed-point iteration scheme. NKA is used while performing steady-state CHT simulations of an air-cooled lithium-ion battery pack, specifically to help accelerate the solution of the solid domain energy equation. The effect of using either isotropic or anisotropic thermal conductivity within the cylindrical lithium-ion battery cells is also evaluated. Results obtained using the NKA accelerator are compared, in terms of accuracy and speed, with those obtained from a traditional nonlinear fixed-point iterative scheme based on successive over-relaxation (SOR). The NKA accelerator is found to perform quite well for the problem at hand, providing results with the specified accuracy, while also being between 5 and 20 times faster than SOR (while solving the solid energy equation). The robust nature of NKA also leads to better global heat balance within the battery pack at all times during the simulation. These observations hold for both the isotropic and anisotropic thermal conductivity conditions. Overall, computational cost reductions of 30–40% are observed when using NKA for the battery pack simulations. Although the performance of NKA is demonstrated for a battery cooling application, NKA performs quite well in other applications also.