A residual linear term is observed in the thermal conductivity of optimally-doped Bi-2212 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 strong 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 dominant, mechanism in suppressing the superfluid density in the cuprate superconductors Bi-2212 and YBCO.