Carbon-based nanostructures are extensively employed as solid additives in nanofluids or polymer matrices for applications in light harvesting, energy conversion and storage. To predict heat transfer in carbonbased nanostructures, a quantitative comprehension of thermal energy exchanges at the interface with their external environment is crucial. The Thermal Boundary Resistance (TBR) stands out as a key parameter hindering efficient thermal energy exchanges between nano-objects and their surroundings. In this work we experimentally determine the TBR for the archetypal case of an interface between multi-wall carbon nanotubes (CNTs) and water. Ultrafast energy exchanges are investigated using femtosecond time-resolved optical spectroscopy. Data rationalization via a thermo-optical model allows retrieval of a CNT/water interface TBR of (4.6 ± 2.2)×10$^{-8}$ m$^2$ K/W. This value constitutes a benchmark for theories aimed at understanding energy transfer between a CNT and water. Notably, the functionalization of the surface of CNTs with covalent groups has been demonstrated to reduce the TBR and facilitate solid-liquid heat exchanges. The measurement and analysis protocol developed in this study is versatile and can be applied to any nanofluid and nanocomposite material.