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The band structures of ordered and thermally disorderedLi$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method. Theunusual, very 1-dimensional band dispersion obtained in previous bandcalculations is confirmed for the ordered structure, and the overall bandstructure agrees reasonably with existing photoemission data. Dispersion andbandstructure perpendicular to the main dispersive direction is obtained. Atemperature dependent band broadening is calculated from configurations withthermal disorder of the atomic positions within the unit cell. This leads aband broadening of the two bands at the Fermi energy which can becomecomparable to their energy separation. The bands are particularly sensitive toin-plane movements of Mo sites far from the Li-sites, where thedensity-of-states is highest. The latter fact makes the effect of Li vacancieson the two bands relatively small. Spin-polarized band results for the orderedstructure show a surprisingly large exchange enhancement on the high DOS Mosites. Consequences for spin fluctuations associated with a cell doubling alongthe conducting direction are discussed.

Effects of thermal- and spin- fluctuations on the band structure of purple bronze Li$_2$Mo$_{12}$O$_{34}$