Is the universe getting warmer due to the light from stars?

Answer

The energy of stars is released in the form of light. In that sense, your question puzzles me a bit. Because the fact that you see stars means that you know what happens to that energy: it is radiated out into the universe, and continues to spread until it is caught by an obstacle (in this case your eye). At that point, the star’s light ‘warms’ your eye a little.

How far the light gets, of course, depends on how much matter there is on the light path. But the fact that we can see very distant galaxies means that the average view in the universe contains little absorbing matter, and the ‘warming’ effect of the starlight is therefore small there.

Most of the starlight is eventually caught by the large and sometimes quite dense interstellar clouds. Where the base temperature of the universe is 2.7K, the temperature of typical interstellar clouds is of the order of 50K, and they get that heat from the radiation of the stars in the galaxy (also partly from the energy of particles flying around the galaxy).

This becomes completely meaningful when new stars are formed in those clouds. In the densest clouds in which the largest stars are formed, the density and size are such that all the light from the stars is absorbed by the cloud; it therefore heats up to temperatures of more than 100K, and emits infrared radiation; and that infrared radiation can penetrate through the cloud. Of galaxies that form many stars, we see almost nothing of the star radiation in its original visible form; almost all radiation is converted into heat radiation from the surrounding cloud! We can then detect that radiation in the (far) infrared, and the ESA satellite Herschel is now doing that in an unparalleled way.