Well, lets go over each one and think of how our body uses each part.
A. If we're cold, there's no reason for it to dilate. When we dilate our vessels, we're going to have more blood flow to that area. We don't want more blood flow to that area why? Because we'll begin to lose heat that way. We will actually vasoCONSTRICT instead to shunt the blood away from the surface to preserve our internal body heat. Therefore, this is NOT an option.
C. Secretion of sebum on the skin is not used to protect against the sun. Our sebum is actually used to keep out bacteria and microorganisms. This is NOT an option.
D. Depending on the wording this one **could** be correct but because it says that it's adding their sweat, that's false. The eccrine and the apocrine glands are two sweat glands, though.
E. Blood vessels near the surface of the skin can dilate, increasing blood flow and heat loss. This is TRUE! In order for us to get rid of some of our heat, the vessels will dilate and causes the blood to enter to the surface of the skin allow the heat to rise up and out and we can get rid of the excess heat.
So, now we've broken them all down, you can see that the only response that is correct is E.