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We present a Monte Carlo simulation designed to predict the vertical velocitydispersion of brown dwarfs in the Milky Way. We show that since these stars areconstantly cooling, the velocity dispersion has a noticeable trend withspectral type. With realistic assumptions for the initial-mass function,star-formation history, and the cooling models, we show that the velocitydispersion is roughly consistent with what is observed for M dwarfs, decreasesto cooler spectral types, and increases again for the coolest types in ourstudy ($\sim$T9). We predict a minimum in the velocity dispersions for L/Ttransition objects, however the detailed properties of the minimumpredominately depend on the star-formation history. Since this trend is due tobrown dwarf cooling, we expect the velocity dispersion as a function ofspectral type should deviate from constancy around the hydrogen-burning limit.We convert from velocity dispersion to vertical scale height using standarddisk models, and present similar trends in disk thickness as a function ofspectral type. We suggest that future, wide-field photometric and/orspectroscopic missions may collect sizable samples of distant ($\sim\!1$ kpc)of dwarfs that span the hydrogen-burning limit. As such, we speculate that suchobservations may provide a unique way of constraining the average spectral typeof hydrogen-burning.

The Effect of Atmospheric Cooling on the Vertical Velocity Dispersion and Density Distribution of Brown Dwarfs