We use a series of N-body/smoothed particle hydrodynamics simulations and analytic arguments to show that the presence of an effective temperature floor in the interstellar medium at T_F ~ 10^4 K naturally explains the tendency for low-mass galaxies to be more spheroidal, more gas rich, and less efficient in converting baryons into stars than larger galaxies. The trend arises because gas pressure support becomes important compared to angular momentum support in small dark matter haloes. We suggest that dwarf galaxies with rotational velocities ~ 40 km/s do not originate as thin discs, but rather are born as thick, puffy systems. If accreted on to larger haloes, tenuous dwarfs of this kind will be more susceptible to gas loss or tidal transformation than scaled-do
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