The nanofluids characterization is of fundamental importance to predict their applicability in a real heat transfer situation. In addition to the transport properties, the nanofluid stability is an important factor to be studied, due to the long pumping, heating, cooling and resting cycles the fluids are usually subjected to. Carbon nanotubes have great potential to be used in nanofluids, due to their high thermal conductivity and low density. However, for aqueous medium, stability requires the use of stabilization methods. This work carried out the study of the transport properties and stability of nanofluids with multiwalled carbon nanotubes (MWCNT), using three stabilization methods: Triton X-100 (TrX-MWCNT) and Arabic gum (AG-MWCNT) as surfactants and functionalized carbon nanotubes with COOH group (COOH-MWCNT). These three nanofluids were compared to investigate the best configuration for heat transfer processes. The thermal conductivity was studied using the hot wire method; rheology was studied through three curves in rotational rheometer of concentric cylinders; specific heat was studied by the differential scanning calorimetry method; density was measured by the Coriolis Effect method; nanoparticles size and zeta potential were measured by the dynamic light scattering method. The COOH-MWCNT nanofluids present the highest thermal conductivity increase reaching 15% at 60 °C and 12% at 30 °C with 1wt% while the A.G-MWCNT and TrX-MWCNT reach 11% and 7.5%, respectively, at 30 °C. A.G-MWCNT nanofluids showed greater stability after long sonication times, while COOH-MWCNT presents best dispersion at 0.125 and 0.25 wt%, from 40 to 160 min of sonication. The specific heat increases with temperature and decreases with MWCNT concentration; however, it presents a peculiar increase in the concentration of 0.25 wt%, increasing about 0.5% and 4.5% for A.G-MWCNT and COOH-MWCNT, respectively at 60 °C. COOH-MWCNT nanofluids showed a thixotropic behavior for 0.5 and 1.0 wt% and large viscosity increase reaching 3.75 and 5.5 times the base fluid viscosity at 5 °C and 60 °C, respectively, with 1 wt%. The nanofluids A.G-MWCNT and COOH-MWCNT present good stability, as well as an increase in transport properties, optimized at a concentration close to 0.25 wt% and the COOH-MWCNT nanofluids can be stabilized simply by changing the water pH.