  In this paper we study several means of compensating for thermal lensing
which, otherwise, should be a source of concern for future upgrades of
interferometric detectors of gravitational waves. The methods we develop are
based on the principle of heating the cold parts of the mirrors. We find that
thermal compensation can help a lot but can not do miracles. It seems finally
that the best strategy for future upgrades (``advanced configurations'') is
maybe to use thermal compensation together with another substrate materials
than Silica, for example Sapphire.
