Transition behavior and thermal properties of a multi-wall carbon nanotube (MWCNT)/nylon-6 composite (P-composite) made by in situ polymerization and subsequently structurally modified by high-pressure–high-temperature treatment have been established. The thermal conductivity (κ) of nylon-6 improved 27% by the addition of 2.1 wt.% MWCNT filler simultaneously as the heat capacity per unit volume decreased 22% compared with that of nylon-6 at 1 atm and 298 K. Moreover, the MWCNT filler raises the glass transition temperature (Tg) of nylon-6, but the pressure dependence of Tg remains unchanged. A model for κ indicates that the interfacial thermal resistance between the MWCNT filler and the nylon-6 matrix decreases 20% up to 1 GPa and most significantly above 0.8 GPa. P-composite was structurally modified by a sluggish cold-crystallization transition at 1.0 GPa, 530 K, which further increased κ by as much as 37% as the crystallinity of nylon-6 improved from 31% to 58% with a preferred crystal orientation and increased crystal size.