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That would provide us information on the effect of random atomic vibrations on the interference pattern, as well as on the states of matter. Did we perform such an experiment? If yes, did we observe anything out of the ordinary?
P.S. Google search did not yield any results. But now, with your contribution, it will, hopefully.
Try googling Xray Diffraction. This is much like a double slit experiment, but with many slits. The space between rows of atoms in a crystal are the slits. These rows run in many directions in 3 dimensions.
Since the slits are the size of the space between atoms, and the wall are made of a plane of atoms, you might expect thermal vibrations to be especially important.
Xray diffraction is an important tool for determining the crystal structure of substances. Many substances undergo phase transitions at various temperatures and pressures. So xray diffraction is done at high and low temperatures. It works fine at these temperatures.
