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A residual linear term is observed in the thermal conductivity of optimally doped Bi 2 Sr 2 CaCu 2 O 8 at very low temperatures whose magnitude is in excellent agreement with the value expected from Fermi-liquid theory and the d-wave energy spectrum measured by photoemission spectroscopy with no adjustable parameters. This solid basis allows us to make a quantitative analysis of thermodynamic properties at low temperature and establish that thermally excited quasiparticles are a significant, perhaps even the dominant, mechanism in suppressing the superfluid density in cuprate superconductors Bi 2 Sr 2 CaCu 2 O 8 and YBa 2 Cu 3 O 7.