Cosmic gravitational background and its temperature There is a cosmic microwave background, according to the Big Bang theory. There is also a cosmic neutrino background, at 1.945 K, yet to be discovered, according to the Big Bang theory. My question is: what is the cosmic graviton/gravitational background temperature?  If any, how could it be related to the neutrino or photon background temperatures?
Remark: Sometimes, some people distinguish between the stochastic gravitational wave background and the so-called primordial gravitational wave events. The answer to this question should also clarify what are these two GW and how could they be related to the hypothetical cosmic gravitational wave background.
 A: It's difficult to say. As @ACuriousMind mentioned in comments, it will be model dependent. Why? Well, look into what fixes the temperature of the  (CMB), made of light. The short version is that the temperature of matter and light were held in lock-step as long as matter consisted of an ionized plasma of mostly hydrogen. Once the electrons and protons combined into neutral hydrogen, an event called recombination, the light and matter were free to evolve separately, with the matter cooling much faster than the light. As a side note, the reason non-relativistic matter cools faster in an expanding universe is because the momentum of the particles goes like $1/a$ (decreases inversely with the scale factor of the universe), both classically and quantum mechanically. Since the kinetic energy of non-relativistic particles is proportional to $p^2$, the temperature of non-relativistic particles will drop like $1/a^2$, whilst relativistic particles drop like $1/a$. 
The temperature at which recombination happens depends on the density of particles in the plasma, and the math (in the Wikipedia article) suggests it happened at a temperature of around $4000\operatorname{K}$.
You can tell a similar story about the cosmic neutrino background (C$\nu$B). Although, Wikipedia's "It is estimated that today, the C$\nu$B has a temperature of roughly $1.95 \operatorname{K}$," should be taken with a grain of salt because we know that neutrinos have a non-zero mass less than $0.120 \operatorname{eV}/\operatorname{c}^2$, which would mean they go non-relativistic somewhere below a temperature of $1400\operatorname{K}$.  Point being, unless their mass is less than $170\operatorname{\mu eV}$, the C$\nu$B is significantly colder than $2\operatorname{K}$.
And that's why the characteristics of any cosmic graviton background will be model dependent. The most critical question being, when, if at all, did it "decouple" from the rest of the matter-energy fields? Since gravity was almost certainly the first field to decouple, you also have to answer thorny question about inflation, the Higgs field, etc, to know its temperature.
