  We discuss the influence of atomic thermal motion on the efficiency of
multimode quantum memory in two configurations: over the free expand of atoms
cooled beforehand in a magneto-optical trap, and over complete mixing of atoms
in a closed cell at room temperature. We consider the high-speed quantum
memory, and assume that writing and retrieval are short enough, and the
displacements of atoms during these stages are negligibly small. At the same
time we take in account thermal motion during the storage time, which, as well
known, must be much longer than durations of all the other memory processes for
successful application of memory cell in communication and computation. We will
analyze this influence in terms of eigenmodes of the full memory cycle and show
that distortion of the eigenmodes, caused by thermal motion, leads to the
efficiency reduction. We will demonstrate, that in the multimode memory this
interconnection has complicated character.
