Fermi Temperature in the modular framework.

A work in progress.

I am trying to understand this formula right now in my framework: 

T_F = frequency / K_Hz

Where:
frequency = Energy_Scale * Density_to_Temperature_Converter
Energy_Scale = (h / (2 * m_e ))
Density_to_Temperature_Converter = particle_density ^ (energy states/ dimensions)
particle_density = 3 * pi^2 * number_of_particles / Volume
energy states =2
dimensions = 3

The part I am having trouble with is understand is how does the energy scale * Density to Temperature Converter becomes a frequency.  The physical reality of the effect.  Mathematically I can see that the units become what they do, but not the why of it.