  Numerical simulations show the formation of self-gravitating primordial disks
during the assembly of the first structures in the Universe, in particular
during the formation of Pop.~III and supermassive stars. Their subsequent
evolution is expected to be crucial to determine the mass scale of the first
cosmological objects, which depends on the temperature of the gas and the
dominant cooling mechanism. Here, we derive a one-zone framework to explore the
chemical evolution of such disks and show that viscous heating leads to the
collisional dissociation of an initially molecular gas. The effect is relevant
on scales of 10 AU (1000 AU) for a central mass of 10 M_sun (10^4 M_sun) at an
accretion rate of 10^{-1} M_sun yr^{-1}, and provides a substantial heat input
to stabilize the disk. If the gas is initially atomic, it remains atomic during
the further evolution, and the effect of viscous heating is less significant.
The additional thermal support is particularly relevant for the formation of
very massive objects, such as the progenitors of the first supermassive black
holes. The stabilizing impact of viscous heating thus alleviates the need for a
strong radiation background as a means of keeping the gas atomic.
