  We show that Fermi repulsion can lead to cored density profiles in dwarf
galaxies for sub-keV fermionic dark matter. We treat the dark matter as a
quasi-degenerate self-gravitating Fermi gas and calculate its density profile
assuming hydrostatic equilibrium. We find that suitable dwarf galaxy cores of
larger than 130 pc can be achieved for fermion dark matter with mass in the
range 70 eV - 400 eV. While in conventional dark matter scenarios, such sub-keV
thermal dark matter would be excluded by free streaming bounds, the constraints
are ameliorated in models with dark matter at lower temperature than
conventional thermal scenarios, such as the Flooded Dark Matter model that we
have previously considered. Modifying the arguments of Tremaine and Gunn we
derive a conservative lower bound on the mass of fermionic dark matter of 70 eV
and a stronger lower bound from Lyman-$\alpha$ clouds of about 470 eV, leading
to slightly smaller cores than have been observed. We comment on this result
and how the tension is relaxed in dark matter scenarios with non-thermal
momentum distributions.
