White hot hydrogen gas, like that during a big bang
(This might get more/better answers on Physics Stack Exchange)

At the high temperatures of the early Big Bang, you have individual protons and electrons, not hydrogen atoms and molecules.  This is because the $kT$ thermal energy is much, much more than the binding energy of the hydrogen atom.

In that case, the moving individual charges create a continuous black body spectrum:


(from Sun.org)

The light will look like a 10,000K source: a bit on the blue side.  But most of the energy will be at wavelengths much shorter than visible light.  The Wien displacement law shows that:

$$\lambda_{\rm{peak}} = {{b}\over{T}} = {{3\times 10^{-3}m \cdot K}\over{1\times 10^6 K}} = 3\times 10^{-9}m$$

A 3nm wavelength corresponds to soft X-rays (or perhaps the very hardest ultraviolet light).  

You'll note that the vertical axis below is logarithmic.  At 100X temperature to the 10000K like, the peak will be at the shorter (left) wavelengths of X rays, but also much higher.  The energy flux goes as $T^4$, so a 100X temperature is a factor of $10^8$ in intensity:  There will be a lot of X rays at these early temperatures.