Yes, chicks can have true fevers where the body is increasing its temperature to fight off disease.
They can also have an increased body temperature for 2 other reasons I can think of off-hand:
-- If the ambient temperature is high (ie they are under a heat lamp, they are in the sun or it is just hot) their temperature will go up. They normally pant to get rid of the excessive heat, but if they are dehydrated or don't feel up to it or it is too humid, the panting wont work as well or not at all and they will be hot.
--They can also get an increase in temperature if there is excessive muscle contraction--faster than they can dissipate the heat (take your temp after jogging or going on a power-walk and you may find your own temperature increased significantly) . If the chick has wry-neck and the muscles are tensing, maybe that's why it seems hot.
I would make sure the little guy is well hydrated and you may want to give it extra energy such as sugar in the water (I like to give them a choice between with or without sugar).
If he has an infection then the fever will help kill off the bacteria. If he continues to go down hill and you feel he is suffering then it would probably be best to cull, as hard as that's going to be.
Good luck.