generally people feel very hot after exercise where as you feel cold after exercise.This is really strange.You should get a thorough checkup to find out the reason behind it.Just consult a doctor and go for the checkup.
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I generally confuse my dr. For a while my bp use to drop while exercising with made me nausea and dizzy. He gave me all type of heart test and all were normal. Eventually he took me off of all med, slowly and one at a time. I stopped getting nausea unless I'm dehydrated.
If you exercise in the heat, it could be an early sign of heat exhaustion. Used to happen to me when i ran. Try working out indoors when it's really bad out, or at least stick to the shade for the most intense bits. Stay hydrated, and dump water over your head every so often. This Florida heat is a bitch.