A model-based information theoretic approach is presented to perform the task of magnetic resonance (MR) thermal image reconstruction from a limited number of observed samples on k-space. The key idea of the proposed approach is to optimally detect samples of k-space that are information-rich with respect to a model of the thermal data acquisition. These highly informative k-space samples can then be used to refine the mathematical model and efficiently reconstruct the image. The information theoretic reconstruction was demonstrated retrospectively in data acquired during MR-guided laser induced thermal therapy (MRgLITT) procedures. The approach demonstrates that locations with high-information content with respect to a model-based reconstruction of MR thermometry may be quantitatively identified. These information-rich k-space locations are demonstrated to be useful as a guide for k-space undersampling techniques. The effect of interactively increasing the predicted number of data points used in the subsampled model-based reconstruction was quantified using the L2-norm of the distance between the subsampled and fully sampled reconstruction. Performance of the proposed approach was also compared with uniform rectilinear subsampling and variable-density Poisson disk subsampling techniques. The proposed subsampling scheme resulted in accurate reconstructions using a small fraction of k-space points, suggesting that the reconstruction technique may be useful in improving the efficiency of thermometry data temporal resolution.