If you'll allow me to be pedantic, they already applied heat to the sample as it was above absolute zero. For this device to not violate the laws of thermodynamics it has to cool down when the power is extracted so, in an otherwise adiabatic system, a perpetual use would eventually require the addition of heat to continue to produce power.

Like the recent claim of a room temperature superconductor, the ability to produce this effect at a macro scale would be revolutionary. Example: 99% efficient solar panels. Combination refrigerator/water heater appliances which use no outside energy. Home heating and cooling which requires not only no energy but produces surplus power in the cooling months. Your home dehumidifier could charge your car or your laptop. You could drop this generator into the ocean and simply pipe unlimited energy to the shore, using the water as a sink. Practically, though, it sounds like microamps (at best) is the result, so - as they said - semi-autonomous, very lower power electronics is the real target application, leaching thermal energy from the environment in such small amounts as to be negligible. A bit like using harvesting energy from radio waves (a myth that was explored on Mythbusters and, while possible, was highly impractical)