Here's my guess:
When a substance changes phases, there is an isothermal reaction that takes place for an extended period of time. This is associated with the energy the substance is taking in, or releasing. If you engineer a substance to have a very long, isothermal phase change, it would be incredibly thermally stable.
There is one hitch, nature likes energy to be at its lowest state. To satisfy this in our application, you would heat this thing up, it would take in energy during this time and if enough heat were supplied, the phase change would take place. Now when you remove the heat, it will be begin to cool at some rate. When it reaches the temperature of the phase change, it will stay there for an extended period of time (this neglects undercooling whis is usually pretty subtle). Once the phase change is over, it will continue to cool.
Below is a graph for the heating of ice to steam. As you can see, there are two isothermal regions, one when ice goes to water, and another when water goes to steam. If you reversed this graph (put the right side of the left and the left side on the right), you would have the time/temperature graph of water cooling from steam to ice.
So basically, these things are most stable at their phase temperature.
And even if my guess is wrong, if I did a good job, you should understand the concept of latent heat.
