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Neat, densely packed, and highly aligned carbon nanotube fibers (CNTFs) have appealing room-temperature axial thermal conductivity (k) and thermal diffusivity (α) for applications in lightweight heat spreading, flexible thermal connections, and thermoelectric active cooling. Although CNTFs are regularly produced from different input carbon nanotubes (CNTs), prior work has not quantified how the CNT molecular aspect ratio r (i.e., molecular length-to-diameter ratio) influences k and α in well-aligned, packed CNTFs. Here, we perform self-heated steady-state and three-omega thermal measurements at room temperature on CNTF suspended in vacuum. Our results show that k increases from 150 to 380W/mK for viscosity-averaged molecular aspect ratios increasing from r=960 to 5600 and nanotube diameters of ∼2 nm, which we attribute to the effects of thermal resistances between CNT bundles. CNTFs made with varying volume fraction ϕ of constituent high-r and low-r CNT have properties that fall within or below the typical macroscopic rule-of-mixtures bounds. The thermal diffusivity α scales with k, leading to a sample-averaged volumetric heat capacity of 1.5±0.3MJ/m3K. This work's findings that fibers made from longer CNT have larger k and α at room temperature motivate further investigation into thermal transport in solution-spun CNTF.