Only objects have temperature - and it's nothing more than a measure of how much vibration energy they have. That's what heat is - just vibration.
If you had a universe full of objects at absolute zero (I think that's what you are describing) all of those objects would be sitting still, unmoving.
If you then shine a light into the universe (You'd have to do it from outside because none of these cold objects have any energy to emit light themselves), the energy of the light would be absorbed by any object it hit, warming it up slightly.
The light (or any other sort of EM radiation) would slowly be converted to a little bit of heat.