Neutron temperature
The neutron temperature, also called the neutron energy, indicates a free neutron's kinetic energy, usually given in electron volts. The term temperature is used, since hot, thermal and cold neutrons are moderated in a medium with a certain temperature. The neutron energy distribution is then adopted to the Maxwellian distribution known for thermal motion. Qualitatively, the higher the temperature, the higher is the kinetic energy of the free neutron. Kinetic energy, speed and wavelength of the neutron are related through the De Broglie relation.

# Neutron energy distribution ranges
Moderated and other, non-thermal neutron energy distributions or ranges are listed in the table below:
- Fast neutrons have an energy greater than 1 eV, 0.1 MeV or approximately 1 MeV, depending on the definition.
- Slow neutrons have an energy less than 1 eV.
- Epithermal neutrons have an energy from 0.025 to 1 eV.
- Hot neutrons have an energy of about .2 eV.
- Thermal neutrons have an energy of about 0.025 eV.
- Cold neutrons have an energy from 5x10-5 eV to 0.025 eV.
- Very cold neutrons have an energy from 3x10-7 eV to 5x10-5 eV.
- Ultra cold neutrons have an energy less than 3x10-7 eV.
- Continuum region neutrons have an energy from 0.01 MeV to 25 MeV.
- Resonance region neutrons have an energy from 1 eV to 0.01 MeV.
- Low energy region neutrons have an energy less than 1 eV.

# Fast neutrons
A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (100 TJ/kg), hence a speed of 14,000 km/s.  They are named fast neutrons to distinguish them from lower-energy thermal neutrons, and high-energy neutrons produced in cosmic showers or accelerators. Fast neutrons are produced by nuclear processes such as nuclear fission.
Neutrons from fusion reactions are usually considerably more energetic than 1 MeV; the extreme case is deuterium-tritium fusion which produces 14.1 MeV neutrons (1400 TJ/kg, moving at 52,000 km/s, 17.3% of the speed of light) that can easily fission uranium-238 and other non-fissile actinides.
Fast neutrons can be made into thermal neutrons via a process called moderation.  This is done with a neutron moderator. In reactors, typically heavy water, light water, or graphite are used to moderate neutrons.

# Thermal neutrons
A thermal neutron is a free neutron with a kinetic energy of about 0.025 eV (approx. 4.0e-21 J; 2.4 MJ/kg, hence a speed of 2.2 km/s) 
which is the most probable energy at a temperature of 290 K (17 C or 62F), the mode (statistics) of the MaxwellBoltzmann distribution for this temperature.
The most probable energy is different from the mean (statistics) energy, which as in any MaxwellBoltzmann distribution is 50% greater than the mode. 
After a number of collisions with nuclei (scattering) in a medium (neutron moderator) at this temperature, neutrons arrive at about this energy level, provided that they are not absorbed.
Thermal neutrons have a different and often much larger effective neutron absorption cross-section for a given nuclide than fast neutrons, and can therefore often be absorbed more easily by an atomic nucleus, creating a heavier - and often unstable - isotope of the chemical element as a result. (neutron activation)

# Fast reactor and thermal reactor compared
Most fission reactors are thermal reactors that use a neutron moderator to slow down, or thermalize the neutrons produced by nuclear fission. This is not primarily to increase the fission cross section for fissile nuclei such as uranium-235 or plutonium-239; it is because uranium-238 has a much lower capture cross section for thermal neutrons, allowing more neutrons to cause fission of fissile nuclei and continue the chain reaction, rather than be captured by 238U.
Fast reactors use unmoderated fast neutrons to sustain the reaction.  However, this requires a higher concentration of fissile material at start-up.  Once started, the high neutron flux in the reactor causes the fertile uranium-238 to capture a neutron and transmute into plutonium-239 which in-turn is fissile.  In this way, excepting initial reactor start-up, a fast reactor can be loaded with unenriched fertile uranium-238, uranium-234 or thorium-232 which are transmuted to "breed" more fissile fuel than the reactor consumes.  When used in this configuration, the reactor is referred to as a fast breeder reactor.  Due to the increased technical complexity of using a working fluid that does not moderate neutrons (inert gas or liquid metal) these reactors are generally reserved for research, production of fissile material for use in nuclear weapons, or transmutation of existing highly radioactive nuclear waste into less radioactive isotopes for safe disposal; not for commercial power generation.