I cannot say for sure, as I am not a medical professional. However, Duke "medical experts" have some interesting thoughts about it:
http://www.dukehealth.org/health_library/health_articles/feed_a_cold
Essentially, what I got from this article is that you should 1)rest, 2)be hygienic, 3)make sure you are getting proper nutrients -- regardless of whether you have the flu or a cold.
I hope that helps!