Again, there's something missing here. When you ask how light heats up a MATERIAL, you asking about a solid object and not "isolated atoms". Please keep in mind that when atoms conglomerate into a solid, in many cases, their "individuality" is lost as far as the property of the material is concerned. This is because the valence shell of each of these atoms are modified, sometime severely, when they are in close proximity with other atoms in forming a solid. This is the origin of the continuos bands that we get in metals, insulators, and semiconductors.
At the SIMPLEST and naive case, one can then picture a solid as a chain of + ions with - charge in between, so you get something like
... + - + - + - + - + ...
This is roughly a highly simplified 1D lattice chain of dipoles. One can then calculate the VIBRATIONAL mode of such a thing. This is where one gets the optical and acoustic modes for the different oscillation. It is the primitive idea of PHONONS.
Now, why am I wasting your time with this? This optical mode is what dictates the optical property of the solid, NOT the "electron transition/absorption" of the individual atom (at least not within the normal visible range). If the phonon mode is available, the EM radiation will be able to oscillate or vibrate the chain and the solid acquires vibrational energy, i.e. HEAT! This makes the material absorbs that particular frequency, causing it to not be completely transparent to that EM radiation, or even be opaque.
Refer to Kittel, or Ashcroft and Mermin texts for a more in-depth discussion on this. In any case, please remember that most of the property of the material you deal with, their properties that you are familiar with are NOT due to the property of the individual, isolate atom of that material. The property of a solid seldom depends on that. It is why Solid State Physics/Condensed matter physics is not the same as atomic/molecular physics. We could study the same based element, but we're studying them under very different characteristics and conditions.
Zz.