Since the discovery of synchrotron X-ray emission from the shell of the supernova remnant (SNR) SN 1006, multiple observations from Chandra and XMM-Newton have shown that many young SNRs produce synchrotron emission in X-rays. Among those, a few peculiar SNRs have their X-ray emission largely dominated by synchrotron radiation, showing no or only faint traces of thermal emission. In this paper, we report our mapping of the thermal emission in three emblematic synchrotron-dominated SNRs: G330.2+1.0, 3C58, and RX J1713.7-3946. We used a blind source separation method able to retrieve faint components from X-ray data in the form of Chandra and XMM-Newton observations. The thermal candidates disentangled by the algorithm were then used to select regions of extraction. We then analyzed the extracted spectra to assess their physical nature. We conclude that the components retrieved by the algorithm indeed represent the spatial distribution of the thermal emission in G330.2+1.0 and 3C58, and a likely thermal candidate in RX J1713.7-3946. Our findings confirm and expand on past studies.