The central compact object XMMU J173203.3−344518 in the supernova remnant HESS J1731−347 challenges conventional neutron star models due to its low mass  and high redshifted surface temperature  eV (). We investigate the observational properties of XMMU J173203.3−344518 within a color-flavor-locked(CFL) phase strange star model. We construct a thermal evolution model of the CFL phase strange star, along with heating due to the viscous dissipation of r-mode oscillations. Employing one of the most widely used quark matter equations of state, we characterize the star properties by the strange quark mass (ms), effective bag constant (Beff), perturbative QCD correction (a4), and pairing gap (Δ). Our analysis demonstrates that the observed properties of XMMU J173203.3344518 can be explained by r-mode heating with a CFL strange star, provided that the initial spin period is shorter than 18 ms. We constrain the r-mode saturation amplitude to 8 × 10−3–1.4 × 10−2 and predict a current spin period of 6–9 ms for an initial period of 1 ms. This rapid rotation is consistent with the absence of detected pulsations. The r-mode instability window remains robust across a wide range of pairing gap values (5–200 MeV),providing a reliable framework for interpretation regardless of microscopic uncertainties. Our results support the identification of XMMU J173203.3344518 as a rapidly rotating,low-mass CFL phase strange star,demonstrating the importance of r-mode heating in the thermal evolution of compact objects with exotic dense matter.

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