We present an analysis of the Far Ultraviolet Spectroscopic Explorer (FUSE) spectrum of HD141569A, a transitional object known to possess a circumstellar disk. We observe two components of gas at widely different temperatures along the line of sight. We detect cold H2, which is thermalized up to J=2 at a kinetic temperature of 51K. Such low temperatures are typical of the diffuse interstellar medium. Since the line of sight to HD141569A does not pass through its disk, it appears that we are observing the cold H2 in a low extinction envelope associated with the high Galactic latitude dark cloud complex L134N, which is in the same direction and at nearly the same distance as HD141569A. The column densities of the higher J-levels of H2 suggest the presence of warm gas along the line of sight. The excitation conditions do not seem to be consistent with what is generally observed in diffuse interstellar clouds. The observed radial velocity of the gas implies that the UV spectral lines we observe are likely interstellar in origin rather than circumstellar, although our absorption line study does not definitely rule out the possibility that the warm gas is close to the star. The discovery of such warm gas along the line of sight may provide evidence for turbulent phenomena in the dark cloud L134N. ; Comment: accepted for publication in A&A