No, since molecules and atoms are still made of something else, and that something else is moving, there is still energy radiating from the system. Unless at some point the universe consists of enclosed systems, completely shielded from everything, then if there's nothing to balance out the outgoing energy, whatever's left floating will radiate energy.
I, myself, believe that all matter in the universe is just energy manifested due to immense speed obtained when at one point the entirety of it exploded. The speed itself is more rotational than directional - the explosion would quickly fall in on itself due to unimaginable mass of the explosion, and the presumed internal limit to speed - it would be slowed, but not stopped, by the same gravity that caused it to collapse and blow in the first place. Anyways. All particles of matter are thus small pockets of energy spinning by themselves, having mass and gravity, and thus keeping the rotating system together, only by virtue of speed. Light is just a form of energy that we can see, and since it travels at light-limit speed, it obtains mass, and clumps together into particles that we see and call photons, but in every other respect it's just energy.
Anyways. Existential and origin-of-the-universe matters aside, is there anything else to discuss in the thread?