Deep neural networks (DNNs) have been widely used for illuminant estimation, which commonly requires great efforts to collect sensor-specific data. In this paper, we propose a dual-mapping strategy-the DMCC method. It only requires the white points captured by the training and testing sensors under a D65 condition to reconstruct the image and illuminant data, and then maps the reconstructed image into sparse features. These features, together with the reconstructed illuminants, were used to train a lightweight multi-layer perceptron (MLP) model, which can be directly used to estimate the illuminant for the testing sensor. The proposed model was found to have performance comparable to other state-of-the-art methods, based on the three available datasets. Moreover, the smaller number of parameters, faster speed, and not requiring data collection using the testing sensor make it ready for practical deployment. This paper is an extension of Yue and Wei [Color and Imaging Conference (2023)], with more detailed results, analyses, and discussions.