  We present the results from three dimensional hydrodynamical simulations of
decaying high-speed turbulence in dense molecular clouds. We compare our
results, which include a detailed cooling function, molecular hydrogen
chemistry and a limited C and O chemistry, to those previously obtained for
decaying isothermal turbulence.
  After an initial phase of shock formation, power-law decay regimes are
uncovered, as in the isothermal case. We find that the turbulence decays faster
than in the isothermal case because the average Mach number remains higher, due
to the radiative cooling. The total thermal energy, initially raised by the
introduction of turbulence, decays only a little slower than the kinetic
energy.
  We discover that molecule reformation, as the fast turbulence decays, is
several times faster than that predicted for a non-turbulent medium. This is
caused by moderate speed shocks which sweep through a large fraction of the
volume, compressing the gas and dust. Through reformation, the molecular
density and molecular column appear as complex patterns of filaments, clumps
and some diffuse structure. In contrast, the molecular fraction has a wider
distribution of highly distorted clumps and copious diffuse structure, so that
density and molecular density are almost identically distributed during the
reformation phase. We conclude that molecules form in swept-up clumps but
effectively mix throughout via subsequent expansions and compressions.
