The thermal conductivity $kappa$ of underdoped Y was measured in the $T to 0$ limit as a function of hole concentration $p$ across the superconducting critical point at $p_{SC}$ = 5.0%. ``Time doping was used to resolve the evolution of bosonic and fermionic contributions with high accuracy. For $p leqslant p_{SC}$, we observe an additional $T^3$ contribution to $kappa$ which we attribute to the boson excitations of a phase with long-range spin or charge order. Fermionic transport, manifest as a linear term in $kappa$, is seen to persist unaltered through $p_{SC}$, showing that the state just below $p_{SC}$ is a thermal metal. In this state, the electrical resistivity varies as log$(1/T)$ and the Wiedemann-Franz law is violated.
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