The thermal conductivity kappa and heat capacity per unit volume rho C-p of triphenyl phosphite (TPP) were measured under different pressure and temperature conditions, and with time during the sluggish liquid to glacial state transformation at temperatures about 15 K above the glass transition temperature. As the transformation slowly proceeds during several hours, rho C-p decreases monotonically from that of the liquid state to a value close to that of the vitrified state. Concurrently, kappa increases nonmonotonically with an intermediate local maximum followed by a minimum, before the final rise to a higher kappa. The properties of the ultimately formed glacial state depend on the thermal history, which implies that the state formed under these conditions is a heterogeneous mixture of nanocrystals and mainly amorphous-like solid, and that the relative amount and microstructure depend on the conditions of the transformation. The nonmonotonic changes in phonon propagation during the liquid to glacial transformation suggest microstructural changes which are consistent with a liquid-liquid transformation and sluggish growth of nanocrystals within amorphous-like solid domains. The isobaric thermal conductivity of the as-formed glacial state shows a reversible step increase, just prior to crystallization on heating, which deviates from the typical behavior of glasses, liquids, and crystals. An increase in pressure shifts the step to higher temperatures and suppresses crystallization, which reveals another reversible rise in kappa and C-p. These results show that increased molecular mobility in the glacial state increases and suggest reduced thermal resistance at boundaries or that the motions carry heat.