Vortex,
I believe that a high giga ohm resistor would produce a
high enough Johnson noise voltage to drive a LED into
light emmission. The LED would get 1 / 2 kTB from ambient.
Therefore an array of billions of very small resistor -
LED pairs would be needed to emit watts of light.
Electrical leakage through air is on a giga ohm scale so
the effect has to be tested in dielectric liquids.
Another way to convert ambient heat into electricity is to
use thermovoltaic cells which are photovoltaic cells for
ambient Infra Red which I believe peaks @ 300K at 10 um.
This may be limited to ~410 watts / M^2 so the cells
should be thin and stacked to improve the power density.
I don't believe that resonance can be built up for Johnson
noise because it is non periodic.
Aloha,
Charlie