The definition of temperature, latent energy, etc.
Temperature describes the average energy in matter. To talk about temperature only makes sense when all molecular degrees of freedom are reasonably equilibrated, including kinetic, vibrational, and rotational degrees of freedom. Molecular collisions very rapidly equilibrate these degrees of freedom and the equilibration between rotation and velocity is actually faster than that between vibration and kinetic energy. It therefore makes no sense to separate out rotation or to claim that rotation is a form of latent energy. While the earth is warmer than space (at a cool 2.7 K, or -270.5 C), all that heat will eventually be re-emitted into space, but fortunately the greenhouse gases in our atmosphere (predominantly water vapor, but unfortunately also CO2) retain the heat from solar absorption long enough to keep us at comfortable temperatures.
Latent energy is energy consumed in a phase transition. E.g., a cooling earth might spend a lot of time at -2 C while all the oceans freeze, emitting a lot of latent heat. Latent heat does not play any role in the understanding of global warming.
In my field of research, we use supersonic molecular beams, expanding a molecular gas into vacuum. Within mm distances from the molecular beam nozzle (microseconds of flight into vacuum), molecules cool from room temperature to few Kelvin. So rotation is not special and equilibrates almost completely within microseconds (faster near room temperature!).
I'll be happy to recommend some textbooks if you want to learn more. I know this stuff pretty well, considering that I develop and perform molecular spectroscopy experiments for a living and teach all aspects of physical chemistry.