  (abridged) The dominant thermal mechanisms in the neutral interstellar
medium, which acts as a star-forming gas reservoir, are uncertain in extremely
metal-poor galaxies. Our objective is to identify the heating mechanisms in one
such galaxy, IZw18, and assess the diagnostic value of fine-structure cooling
lines. We also seek to constrain the mass of H$_2$, which, despite being an
important catalyst and tracer of star formation, remains elusive in this
object. Building on a previous photoionization model within a multi-sector
topology, we provide additional constraints from the [CII] and [OI] lines and
the dust mass recently measured with Herschel. The heating of the HI region
appears to be mainly due to photoionization by radiation from a bright X-ray
binary source, while photoelectric effect (PE) is negligible. The [CII] and
[OI] lines imply an average X-ray luminosity of $4\times10^{40}$ erg s$^{-1}$,
while the [NeV] upper limits bring strong constraints to the soft X-ray flux
arising from the binary. A negligible amount of H$_2$ is predicted, but
$\lesssim10^7$ M$_\odot$ of H$_2$ may be hidden in sufficiently dense clouds of
order $\lesssim10$ pc in size. Regardless of the presence of significant
amounts of H$_2$, [CII] and [OI] do not trace the so-called CO-dark gas, but
the almost purely atomic medium. Although the [CII]+[OI]/TIR ratio is close to
values found in more metal-rich sources, it cannot be safely used as a PE
heating efficiency proxy. This ratio seems to be kept stable due to a
correlation between the X-ray luminosity and the star-formation rate. We
propose that X-ray heating is an important process in extremely metal-poor
sources. The weak PE heating due to the low dust-to-gas ratio could be
compensated for by the larger occurrence and power of X-ray binaries in
low-metallicity galaxies. We speculate that X-ray heating may quench star
formation.
