Is that normal? Am I the odd one out?
Thermal sensitivity is often linked with Irritable Bowel Syndrome, though to my knowledge it alone doesn't mean it is IBS. But even if it only occurred to be people with IBS, IBS is not an uncommon condition.
I experience it, I have to brace in midsummer when entering the freezer isles. As for what it feels like? Sudden onset explosive diarrhea. Except it won't actually be diarrhea. Actually you may not expel anything. It can basically be your ass's way of 'Dry Heaving'. If you try and ignore it you can quickly end up shaking and sweating all over the place while trying to not shit yourself, it is pretty awful honestly. For me guzzling Icewater and sometimes Popsicles can also do it(again midsummer when temps are around 100F). Basically anything that RAPIDLY cools the bowels down can cause them to basically start having muscle spasms. Good news is if you can weather it it will pass once everything levels back out temp wise. It just isn't pleasant.