  We investigate the finite temperature momentum distribution of bosonic
noncondensate particles inside a 3D optical lattice near the superfluid to Mott
insulator transition point, treating the quantum fluctuation and thermal
fluctuation effects on equal footing. We explicitly address the different
momentum ($q$) dependence of quasi-particles excitations resulted from thermal
and quantum origin: the former scales as $|\bfq|^{-2}$ and hence is dominant in
the small momentum region, while the later scales as $|\bfq|^{-1}$ and hence
dominant in the large momentum limit. Analytic and semi-analytic results are
derived, providing a unique method to determine the temperature, condensate
density, coherent length and/or single particle gap etc. inside the optical
lattice. Our results also agree with the scaling theory of a quantum $XY$ model
near the transition point. Experimental implication of the TOF measurement is
also discussed.
