  The first interstellar object observed in our solar system, 1I/`Oumuamua,
exhibited several peculiar properties, including extreme elongation and
non-gravitational acceleration. Bergner and Seligman (hereafter BS23) proposed
that evaporation of trapped H$_2$ created by cosmic rays (CRs) can explain the
non-gravitational acceleration. However, their modeling of the thermal
structure of 1I/`Oumuamua ignored the crucial cooling effect of evaporating
H$_2$. By taking into account the cooling by H$_2$ evaporation, we show that
the surface temperature of H$_2$-water ice is a factor of 9 lower than the case
without evaporative cooling. As a result, the thermal speed of outgassing H$_2$
is decreased by a factor of 3. Our one-dimensional thermal modeling that takes
into account evaporative cooling for two chosen values of thermal conductivity
of $\kappa=0.01$ and $0.1$ WK$^{-1}$m$^{-1}$ shows that the water ice volume
available for H$_2$ sublimation at $T>30$ K would be reduced by a factor of 9
and 5 compared to the results of BS23, not enabling enough hydrogen to propel
1I/`Oumuamua.
