Fluid phase transitions inside single, isolated carbon nanotubes are predicted to deviate substantially from classical thermodynamics. This behaviour enables the study of ice nanotubes and the exploration of their potential applications. Here we report measurements of the phase boundaries of water confined within six isolated carbon nanotubes of different diameters (1.05, 1.06, 1.15, 1.24, 1.44 and 1.52 nm) using Raman spectroscopy. The results reveal an exquisite sensitivity to diameter and substantially larger temperature elevations of the freezing transition (by as much as 100 degrees C) than have been theoretically predicted. Dynamic water filling and reversible freezing transitions were marked by 2-5 cm(-1) shifts in the radial breathing mode frequency, revealing reversible melting bracketed to 105-151 degrees C and 87-117 degrees C for 1.05 and 1.06 nm single-walled carbon nanotubes, respectively. Near-ambient phase changes were observed for 1.44 and 1.52 nm nanotubes, bracketed between 15-49 degrees C and 3-30 degrees C, respectively, whereas the depression of the freezing point was observed for the 1.15 nm nanotube between -35 and 10 degrees C. We also find that the interior aqueous phase reversibly decreases the axial thermal conductivity of the nanotube by as much as 500%, allowing digital control of the heat flux.