From their website, it is clear that a Burnout mug is firstly a normal thermos mug, but with an added layer filled with phase-changing material (PCM). Therefore, so far as keeping the heat in, it functions exactly like a normal thermos mug these guys are talking about.
However the added PCM layer will firstly absorb the excessive heat quickly to cool the beverage down to optimal drinking temperature, and then keep this amount of heat within it through changing its state (or change of phase, like when water boils to absorb heat to become steam).
Acorrding to thermodynamics, this amount of heat cannot just disappear, so it keeps the beverage at the constant temperature by gradualy releasing the heat back to the beverage - kind like have a built-in heater - untill all heat is used up and the PCM goes back to its original phase.
Therefore, scientifically, Burnout mugs should keep the beverage - at a designed optimal drinking temperature - longer than a normal thermos mug.
