  We study the clustering properties of the galaxy clusters detectable for the
Planck satellite due to their thermal Sunyaev-Zel'dovich effect. We take the
past light-cone effect and the redshift evolution of both the underlying dark
matter correlation function and the cluster bias factor into account. A
theoretical mass-temperature relation allows us to convert the sensitivity
limit of a catalogue into a minimum mass for the dark matter haloes hosting the
clusters. We confirm that the correlation length is an increasing function of
the sensitivity limits defining the survey. Using the expected characteristics
of the Planck cluster catalogue, which will be a quite large and unbiased
sample, we predict the two-point correlation function and power spectrum for
different cosmological models. We show that the wide redshift distribution of
the Planck survey, will allow to constrain the cluster clustering properties up
to z=1. The dependence of our results on the main cosmological parameters (the
matter density parameter, the cosmological constant and the normalisation of
the density power-spectrum) is extensively discussed. We find that the future
Planck clustering data place only mild constraints on the cosmological
parameters, because the results depend on the physical characteristics of the
intracluster medium, like the baryon fraction and the mass-temperature
relation. Once the cosmological model and the Hubble constant are determined,
the clustering data will allow a determination of the baryon fraction with an
accuracy of few per cent.
