That's an excellent idea. The only drawback is you have to remember it's a "surge" solution. It keeps your device cool for a while, but if you leave the device on too long, it will heat up.
You could use this to have a short term "turbo mode" where you have a higher power mode, but you can only use it at that mode for a while. The phase-change heat sink would increase the time before it overheats. Some devices have this "turbo" mode already, even if they don't admit it, since they will overheat if left on for too long.
The other advantage would be to reduce the junction temp on a semiconductor device in normal usage to extend the lifetime. Even if you don't immediately burn the device out from the temperature reached, reducing the max temperature most of the time you use the device may extend the lifetime due to "degree-hours." You might also get some increased lifetime due to mechanical stress from thermal cycling because the peak temperature is lower for most of the times you turn the device on.
You'd need to consider thermal expansion, but that shouldn't be too hard. You could have a mechanically expandable reservoir with something like a dome that flexes like the bottom of an old style oil can. You could also simply have some air space in the reservoir so that a gas could take up the expansion of the phase change material.
Presumably, you could tailor the transition temperature by having a material that's a mix of two materials with different melting points. You'd have to use materials that didn't separate with the melt/freeze cycle.
One thing I wonder is if you can get enough material in a small enough space to be worth the effort from a practical sense.