Do you really shiver, though, if only the surface of your skin is cold? I only shiver when my core temp is cold - never when I feel warm and only my skin is cold. If I'm physically exerting myself outside in winter and I get hot and take off my jacket, my sweaty skin is cold but body temp is still hot from exertion, I don't shiver. When my mom put me in an ice cold bath when I had a fever above 104 when I was 9 my skin was freezing but I didn't shiver because my core temp wasn't below normal. Even if I did start shivering, it would only be because my core temp was getting too cold and then that would be a good thing because it would be my body protecting itself from a dangerously cold temperature extreme. Your body wouldn't continue shivering to the point that you overheated yourself again, you'd just shiver until your core temp normalized and then your body would have done exactly what it was supposed to do - protect your brain and other organs from extreme temps... I guess there is danger if you leave an incapacitated person in a ice bath for a long time, but I'm talking about when it is an emergency and someone is at risk of cooking their organs from heatstroke.

The body has another natural protection against rapid swings in temp - blood vessels at the skin constrict to protect the core from excessive cold, so the colder your skin and body get the less the cold is transferred to your core because your blood has less contact with the cold skin... when you're overheated, your hot internal temp keeps the vessels more dilated than they would normally be given exposure to the cold treatment, but as your core temp drops the vessels will constrict more and the effect of the cold treatment on your core temp is less pronounced. The body has these natural protection mechanisms that protect you from rebounding too quickly. Bottom line, if someone is shivering, take them out of the ice bath or stop the application of alcohol because their core temp has dropped sufficiently.