Carbon nanotubes (CNTs) are potential candidates to enhance the heat balance of concrete, reducing internal stresses caused by differential heating in massive concrete elements. The higher the aspect ratio (AR) and content of CNTs, the greater the expected thermal conductivity (TC). However, high AR may impair the proper dispersion of CNTs in cementitious matrix, potentially harming the workability and mechanical strength of the composite. This work evaluated the effect of the AR (35, 250, 900, and 3500) and content (0.05% and 0.10%) of CNTs on the TC, rheology (squeeze flow), and mechanical strength of cement paste. Results showed that 0.05% CNT increased the TC of paste by up to 15% for AR of 250, but further increasing AR progressively reduced the TC of the composite. In turn, 0.10% CNT incorporation did not result in significant TC gains. The yield stress and viscosity of the mixes progressively increased as CNTs content and AR increased, by up to 119% compared with plain cement paste. No significant differences were observed in 28-day compressive strength with 0.05% CNT incorporation, while 0.10% CNT led to slight strength reductions for some mixes. Regarding flexural strength, 0.05% incorporation of either CNT decreased the strength of the mixes while 0.10% incorporation generally compensated this reduction, except for the lowest aspect ratio. Overall, CNTs with intermediate AR (around 250) was effective in improving the thermal conductivity of cement paste, increasing it by 15% with relatively low content (0.05%) while did not significantly impair the fresh and mechanical performance of the composite.