  We exactly calculate the particle number $N$ of scalar fields which are
created from an initial vacuum in certain higher-dimensional cosmological
models. The spacetimes in these models are the four-dimensional Chitre-Hartle
or radiation-dominated universe with extra spaces which are static or power-law
contracting. Except for some models in which no particles could be produced,
the distribution of created particles shows a thermal behavior, at least in the
limit of high three-dimensional "momentum" $k$. In some models, $N$ does not
depend on the magnitude of the extra-dimensional "momentum" $k_c$ if $k_c$ is
nonvanishing. A cutoff momentum $k_c$ may emerge in some models, and particles
with $k\le k_c$ could not be produced. We also discuss these results.
