ABSTRACT Dark matter (DM) as a pressureless perfect fluid provides a good fit of the standard Λ cold dark matter (ΛCDM) model to the astrophysical and cosmological data. In this paper, we investigate two extended properties of DM: a possible time dependence of the equation of state of DM via Chevallier–Polarski–Linder parametrization, wdm = wdm0 + wdm1(1 − a), and the constant non-null sound speed $\hat{c}^2_{\rm s,dm}$. We analyse these DM properties on top of the base ΛCDM model by using the data from Planck cosmic microwave background (CMB) temperature and polarization anisotropy, baryonic acoustic oscillations (BAOs), and the local value of the Hubble constant from the Hubble Space Telescope (HST). We find new and robust constraints on the extended free parameters of DM. The most tight constraints are imposed by CMB+BAO data, where the three parameters wdm0, wdm1, and $\hat{c}^2_{\rm s,dm}$ are, respectively, constrained to be less than 1.43 × 10−3, 1.44 × 10−3, and 1.79 × 10−6 at 95 per cent CL. All the extended parameters of DM show consistency with zero at 95 per cent CL, indicating no evidence beyond the CDM paradigm. We notice that the extended properties of DM significantly affect several parameters of the base ΛCDM model. In particular, in all the analyses performed here, we find significantly larger mean values of H0 and lower mean values of σ8 in comparison to the base ΛCDM model. Thus, the well-known H0 and σ8 tensions might be reconciled in the presence of extended DM parameters within the ΛCDM framework. Also, we estimate the warmness of DM particles as well as its mass scale, and find a lower bound: ∼500 eV from our analyses.