Impedance-based temperature detection (ITD) is a promising approach for rapid estimation of internal cell temperature based on the correlation between temperature and electrochemical impedance. Previously, ITD was used as part of an Extended Kalman Filter (EKF) state-estimator in conjunction with a thermal model to enable estimation of the 1-D temperature distribution of a cylindrical lithium-ion battery. Here, we extend this method to enable estimation of the 2-D temperature field of a battery with temperature gradients in both the radial and axial directions. An EKF using a parameterised 2-D spectral-Galerkin model with ITD measurement input (the imaginary part of the impedance at 215 Hz) is shown to accurately predict the core temperature and multiple surface temperatures of a 32,113 LiFePO4 cell, using current excitation profiles based on an Artemis HEV drive cycle. The method is validated experimentally on a cell fitted with a heat sink and asymmetrically cooled via forced air convection. A novel approach to impedance-temperature calibration is also presented, which uses data from a single drive cycle, rather than measurements at multiple uniform cell temperatures as in previous studies. This greatly reduces the time required for calibration, since it overcomes the need for repeated cell thermal equalization.