  We calculate the surface temperature and the resulting brightness of
sub-relativistic objects moving through the Solar system due to collisional
heating by gas and radiative heating by solar radiation. The thermal emission
from objects of size $\gtrsim 100$ m and speed of $\gtrsim 0.1c$, can be
detected by the upcoming {\it James Webb Space Telescope} out to a distance of
$\sim 100$ au. Future surveys could therefore set interesting limits on the
abundance of fast-moving interstellar objects or spacecraft.
