[mostly_harmless]

Not quite. They are taking advantage of the fact that matter takes (or releases) a lot more energy when it is changing state(eg. solid to liquid), then when it is simply changing temperature in the same state.

for example, water takes about 75J to heat one mol by 1K. but it takes about 285000J to change one mol of ice to one mol of water

So, they have this lump of metal, that has a core of some other material that presumably changes state at the preferred temperature of coffee. What this means is that when the coffee is hotter than the joulies, the core melts absorbing a lot of energy. Then when the coffee is cooler than the preferred temperature, the core of the joulies re-solidifies, releasing a lot of energy, keeping the coffee warm.