The previous answer really isn't a very good one.
Your question has a very complicated answer.
In molecules, electrons inhabit different molecular energy levels. When exposed to some form of radiation, the electrons can change their energy level.
Now, a quantum mechanical rule says that an electron can only change its energy if it receives an amount of energy from a photon of exactly the correct energy to account for the difference between its current energy level, and the excited state energy level.
Now, because a photon is a quanta of electromagnetic radiation, its energy and its frequency are proportional (by Planck's constant). Hence, only photons of EMR of particular wavelengths can affect particular molecular excitations. Now, different molecules have different molecular energy levels, changing anything about the molecule's structure will change these levels accordingly.
When we see colour, we are detecting photons of the correct frequency to be identified as, say, blue. Take for example a pair of jeans.
The dye in the jeans will absorb a mixture of photons corresponding to the energy transition gap between the highest occupied molecular energy level and the lowest unoccupied molecular energy level. Because they look blue, we know that there is no energy gap whose energy is equal to the frequency of blue light multiplied by Plank's constant. As the photon is not absorbed by the jeans, then it is just reflected. So yes, it is "rejected", after a fashion. It simply doesn't interact with the electrons.
"Heat" is a part of the electromagnetic spectrum, remember. -Infrared.