Thermal conductivity and specific heat were measured in the superconducting state of the heavy-fermion material Ce(1-x)La(x)CoIn5. With increasing impurity concentration x, the suppression of T(c) is accompanied by the increase in residual electronic specific heat expected of a d-wave superconductor, but it occurs in parallel with a decrease in residual electronic thermal conductivity. This contrasting behavior reveals the presence of uncondensed electrons coexisting with nodal quasiparticles. An extreme multiband scenario is proposed, with a d-wave superconducting gap on the heavy-electron sheets of the Fermi surface and a negligible gap on the light, three-dimensional pockets.