  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.
