No, the characteristics will not be passed on to his offspring.
The second degree burns over most of his arms and legs WILL NOT be passed on to his offspring.
The reason why "no" would be the correct answer is because the second degree burns that the student would not be genetically affected.
Burns on your skin will not genetically impact the student, due to the fact that the burns would only apply to the person, not the offspring. Burns would affect the "physical appearance" of the student, but won't affect the physical appearance of the offspring, since there's no way the burns could be passed on to the offspring.
If the person were to ever have an offspring, the offspring will not have burns around their arms and legs, due to the fact that the burns don't affect the genetic system of the student. The student would have the burns, but the offspring will not.