In a comprehensive investigation of carbon nanotube (CNT) filled liquid and solid polybutadienes of molecular weights 2600 and 100 000, respectively, we report results of thermal conductivity (k), glass transition temperature (T g ), interfacial interaction and microstructure before and after simultaneous highpressure and high-temperature (HP&HT) treatment. The HP&HT treatment changed polybutadiene from a liquid or solid to a highly cross-linked, ebonite-like, state. Concurrently, the microstructure changed from randomly dispersed CNTs to a web-like structure of coated and/or wrapped CNTs, with a permanent shift in their D*-band by as much as $16 cm À1 . Moreover, k of the recovered state of a 2.9 wt% -COOH functionalized multi-wall carbon nanotube (MWCNT) composite increased by $34% predominantly due to an irreversible densification and a consequentially increased phonon velocity. Results prior to treatment show that single-wall carbon nanotube (SWCNT) fillers promote k better (17%/wt%) than -SH functionalized MWCNT fillers (8%/wt%), which is accounted for by their higher aspect ratio, whereas their about twice as high k appears to be unimportant. The SWCNTs also raise T g slightly more than MWCNTs and, in particular, under the most densified conditions and for the high molecular weight polybutadiene, which may be due to more favorable conditions for coating/wrapping.