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.

Weekend projects come and go with hardly a whimper. The hard part comes when you want to turn that weekend project into something people will actually use (or in this case, pay for). Creating a compelling brand, crafting a marketing message that resonates, designing the product so that it "feels" good to use, engineering something durable and long lasting, scaling to meet demand et al? These things require a heck of a lot more than a class in thermodynamics.

Regardless, the market has spoken and 300+ people saw enough value in this thermal mass to support it.

What the Joulies do is _cool_ the coffee by initiating a phase change in their PCM, but then don't drop it too far down.

They actually actively maintain the temperature until their internal substance has turned back into a solid (which may or may not be what you meant).