A little below 2 kelvins, superfluid helium conducts heat better than copper, which is yet an excellent conductor. The reason is that thanks to superfluidity, liquid can easily move from hot zones to cold zones, enabling a thermal conduction by convection, a phenomenon much more efficient than the usual gradual heat diffusion. When you put a saucepan of water on a hotplate, the bottom is hotter than the free surface. Bubbles appear in the bottom, get bigger, get loose and spread over the water: the water is boiling.
However, in superfluid helium, the great thermal conduction requires a very homogeneous temperature everywhere. In the absence of zones hotter than others, the transformation from liquid to vapour can only happen at the free surface where helium evaporates: there are no bubbles. Superfluid helium vaporizes without boiling. This property is visible to the naked eye: when liquid helium is pumped in order to be cooled, the boiling phenomenon disappears at 2.17 K and the quantum order settles whenever the normal liquid becomes superfluid (cf figure below).
These two images come from the film "Superfluid Helium" by JF Allen and JMG Armitage (St Andrews University 1982). The above image shows liquid helium at 2.4 K, as the thermometer needle on the left indicates. The bottom image is taken at 2.1 K, below the transition temperature to the superfluid state, and there is no boiling (although it keeps vaporizing).
