Hot atomic hydrogen shows up from its optical emission lines, which are excited in material at ~10^3 K.
However, most of space is much cooler than 10^3 K, so optical lines are not seen.
In 1944, van de Hulst pointed out that there is a hyperfine transition in hydrogen in which the relative spins of the proton and electron change direction:
This transition might then be observable via the 21cm radiation that it produces.
The transition is strongly forbidden (it fails to conserve spin), and so has a very long lifetime (~10^7 years). It is therefore much more likely that an excited atom will be collisionally de-excited.
However, there is so much atomic hydrogen out there that significant amounts of 21cm radiation are emitted.
This emission has proved crucial in developing our understanding of the galactic rotation curve