  Two-dimensional CP**(N-1) models are used to compare the behavior of
different cooling techniques on the lattice. Cooling is one of the most
frequently used tools to study on the lattice the topological properties of the
vacuum of a field theory. We show that different cooling methods behave in an
equivalent way. To see this we apply the cooling methods on classical
instantonic configurations and on configurations of the thermal equilibrium
ensemble. We also calculate the topological susceptibility by using the cooling
technique.
