The non-destructive measurement of electrical polarization and space charge densities is a key technique in electret research. The principal idea behind these methods is a non-uniform deformation or heating, which gives rise to a short-circuit current that can be recorded in the time or frequency domain, and which carries information about the polarization depth profile. In recent years, thermal pulses and thermal waves have been used successfully to obtain three-dimensional polarization maps in polymeric electrets by scanning the beam of a pulsed or intensity-modulated cw laser across the sample surface. However, the polarization maps in these experiments were reconstructed using a relatively simplistic one-dimensional heat diffusion model that does not take into account lateral heat diffusion in the metal electrode. A two-dimensional "coupled neighbors" model was developed, where the current signal from several adjacent beam pointings along a scan line is coupled together, and a Monte Carlo method is used for the deconvolution. Simulations show that the new approach enhances the lateral resolution by a factor of 2 - 3 ×, since it avoids the information loss occurring when three-dimensional polarization measurements are processed with a one-dimensional thermal model. We also present an augmented, low-noise thermal-pulse instrument where thermal pulses are initiated by a pulse-modulated diode laser.