Is there a mathematical relationship between energy (in keV) and temperature (K)?

Answer 1

Room temperature is about 1/30 eV. So 300 K is roughly 0.03 eV, and1 eV about 10000 K.

It's simpler if you relate energy in eV and temperature in kK.

Answer 2

Yes, using Boltzmann's constant, k, which has units of energy / temperture. It's value can be found here:

http://pdg.lbl.gov/2007/reviews/consrpp.pdf

This arises frequently in statistical mechanics. For example, the energy E of a monatomic ideal gas of N particles at temperature T is given by

E = 3/2 * N * k * T