Ignition Problems with '87 5.0. HELP!!!

[Holly]

My '87 5.0 doesn't start when it is cold (40-65 degrees). This has become a pain in the butt. It always starts when it is warm (65+ degrees). I gave my car a tune up 3 weeks ago (changed the distributor, rotor, sparkplugs and wires, and fuel filter) hoping this would change the condition; however, no luck. I keep all fluid levels maintained as well. I have a Chilton's guide and I looked at the ignition diagram and I'm thinking it might be the starter or the "ignition module." The problem is I don't know what the heck an "ignition module" does. The book says it controls the start of the engine in "certain conditions." Does the ignition module need to be replaced? The '87 5.0 has a duraspark type two ignition system. Has anyone had similar problems with their mustang and fixed it? I would greatly appreciate any advice or help. Thank you.