I'm thinking of high-frequency transistors / ICs with heatsinks and a bank of these lights being attached.
It wouldn't be a primary cooling method, but if you needed a light on your device anyways then you could make use of this mechanism as well. Imagine backlights for LCDs in mobile devices. An iPad or Android tablet can easily reach 100 F when playing games, and for most cases that's warmer than ambient air temperature.
I don't have access to the original paper (haven't checked arxiv yet). Do the lights need to be at a certain temperature for this to work at all? I know that in similar experiments (condensates) the lattice vibrations only propagate at temperatures much lower than 70 F. At room temperature there is too much chaotic motion in the structure. I'd see that as a major limitation on scale and real-world application.