Only in the load resistor. Electron flux in the graphene membrane appears to be solely due to geometry. This curvature does not necessarily need to be buckled via heat energy. It could be mechanical or electrical, if I understand things correctly...
More detail in this video clip with UArk's Paul Thibado:
https://www.youtube.com/watch?v=wrleMqm3HiU
I think what this research opens up is the possibility of "optimal" harvesting. There is some resonant frequency, some circuit configuration yet to be discovered that is perhaps self-sustaining. They've chosen "stochastic thermodynamical" circuits because its low hanging fruit. But it seems really exciting to me. Almost like a third class of energy production after solar and hydrogen (where 99% of research funds are allocated). Ocean wave energy harvesting perhaps?
In any case, congrats to the researchers on their painstaking hard work ;)
Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
https://arxiv.org/abs/2002.09947