Aims.The nature of Cygnus X-3 is still not understood well. This binary system might host a black hole or a neutron star. Recent observations by INTEGRAL have shown that Cygnus X-3 was again in an extremely ultrasoft state. Here we present our analysis of the transition from the ultrasoft state, dominated by blackbody radiation at soft X-rays plus non-thermal emission in the hard X-rays, to the low hard state. Methods.INTEGRAL observed Cyg X-3 six times during three weeks in late May and early June 2007. Data from IBIS/ISGRI and JEM-X1 were analysed to show the spectral transition. Results.During the ultrasoft state, the soft X-ray spectrum is well-described by an absorbed ($N_{\rm H} = 1.5$ $\times$ $10^{22}~\rm cm^{-2}...