The intensifiacation of convective heat transfer by nanofluids based on isopropyl alcohol and ethylene glycol with carbon nanotubes in a cylindrical channel with a heat flow of constant density at the channel wall was investigated. It was established experimentally that the indicated nanofluids are pseudoelastic and, therefore, their rheology is well defined by the model of a power-law fluid. It is shown that the velocity of flow of such a nanofluid in the region of the channel wall is increased, and the velocity profile of this flow is flattened. The indicated effect enhances with increase in the concentration of carbon nanotubes in the nanofluid. It was established that the deformation of the velocity profile of the nanofluid leads to an increase in its heat transfer coefficient, which is one of the mechanisms of intensification of convective heat transfer by nanofluids with carbon nanotubes. The increase in the heat transfer coefficient of a nanofluid, as compared to that of its base fluid, is especially large for the nanofluids with single-walled carbon nanotubes. In the case of their concentration 0.25% in a nanofluid based on isopropyl alcohol, the heat transfer by the nanofluid is larger by 2.7 times that the heat transfer by its base fluid, and the coefficient of thermohydraulic efficiency of the nanofluid flow at small Reynolds numbers can reach 3.5.