The thermal conductivity κ, heat capacity per unit volume ρcp and glass transition behaviour under pressure have been established for medium and high vinyl content polybutadiene PB with molecular weights 2600 and 100 000 and their highly cross-linked (ebonite) states obtained purely by high-pressure high-temperature treatments. Cross-linking eliminates the glass transitions and increases κ by as much as 50% at 295 K and 1 atm, and decreases ρcp to a limiting level close to that of the glassy state of PB, which is reached before the ultimate cross-link density is achieved. The pressure and temperature behaviours of κ are strongly changed by cross-links, which increases the effect of temperature but decreases the effect of pressure. We attribute these changes to a cross-linked induced permanent densification and consequential increase of phonon velocity simultaneously as conduction along polymer chains is disrupted. The glass transition temperatures for a time scale of 1 s are described to within 0.5 K by: Tg(p) = 202.5 (1 + 2.94 p)0.286 and Tg(p) = 272.3 (1 + 2.57 p)0.233 (p in GPa and T in K) up to 1 GPa, for PB2600 and PB100000, respectively, and can be estimated for medium and high vinyl content PBs with molecular weights in between by a constant, pressure independent, shift in temperature.