  We investigate the properties of thermal abelian magnetic monopoles in the
high temperature phase of Yang--Mills theories, following a recent proposal for
their identification on lattice configurations. The study is done for SU(2)
pure gauge theory, for temperatures going up to about 10 times the deconfining
temperature and using the Maximal Abelian gauge to perform the abelian
projection. We find that the monopole density has a well defined continuum
limit. Its temperature dependence disagrees with a free particle gas prediction
and is instead well described by a $T^3/(\log (T/\Lambda))^\alpha$ behaviour in
all the explored range, with $\alpha \sim 2$ and $\Lambda \sim 100$ MeV. Also
the study of spatial correlations of thermal monopoles shows the presence of
non-trivial interactions among them. Finally, we discuss the gauge dependence
of our results, showing that it is significant and that, even within the
Maximal Abelian gauge, Gribov copy effects are important.
