>Superfluid helium's maximum thermal conductivity is roughly 100x diamond's maximum!

Never thought about this before. Would that mean that heat propagates much more quickly? Possibly even approaching the speed of sound of the material?

Thermal conductivity measures the heat flux given a temperature gradient. That is, how fast heat energy flows across a surface, given a certain temperature gradient across it.

It has nothing to do with the velocity of the heat carriers themselves (phonons, or charged particles).

E.g. phonons always travel at the speed of sound, in any material.

Slide 12. Pretty much yeah. https://indico.cern.ch/event/1541024/attachments/3055157/540...

You can kind of isolate the different vibrational modes and their corresponding energy transmission. "Phonons" are basically sound waves (the particle analogue), labeled in figure 2: https://www.nist.gov/system/files/documents/2019/07/12/dcs_2...