  This Letter investigates the amount of dust in the intergalactic medium
(IGM). The dust photoelectric heating can be the most efficient heating
mechanism in the IGM where the density is very small and there are a lot of
hard ultraviolet photons. Comparing the observational thermal history of IGM
with a theoretical one taking into account the dust photoelectric heating, we
can put an upper limit on the dust-to-gas ratio, ${\cal D}$, in the IGM. Since
the rate of the dust photoelectric heating depends on the size of dust, we find
the following results: If the grain size is $\ga 100$ \AA, ${\cal D}$ at $z
\sim 3$ is $\la 1/100$ Galactic value corresponding to $\Omega_{\rm dust}^{\rm
IGM}\la 10^{-5}$. On the other hand, if the grain size is as small as $\sim 10$
\AA, ${\cal D}$ is $\la 1/1000$ Galactic value corresponding to $\Omega_{\rm
dust}^{\rm IGM}\la 10^{-6}$.
