The thermal conductivity kappa of underdoped YBa2Cu3Oy was measured in the T-->0 limit as a function of hole concentration p across the superconducting critical point at pSC identical with 5.0%. The evolution of bosonic and fermionic contributions to kappa was tracked as the doping level evolved continuously in each of our samples. For p< or =pSC, we observe a T3 component in kappa which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, observed as a T-linear term in kappa which persists unaltered through pSC, violates the Wiedemann-Franz law, since the electrical resistivity varies as log(1/T) and grows with decreasing p.