I can confirm this as well. I had messages about my character getting hyperthermia and it also said it was cold on the previous line. I will try to get a screenshot of this.

maybe it's because of the weather?
I mean... Sunny, you are running around the map, actually it is sport.
When you make Sport on a warm sunny day with a vest, a heyvy full backpack, with heavy hot cargo pants, maybe with a raincoat and a hat, then I'm sorry... but actually if you are not a special unit of the Marine Corps you will pass out^^

To be honest, when I had the message I was wearing a puffer jacket. However, the weather was the crazy DayZ rain system and it was raining a ton. My character even complained about it being "quite cold out there" while it was complaining about the over heating... So something is wrong. I never passed out, I stripped down ran into the rain and never dried myself off. The hyperthermia messages stopped at that time. I even abandoned the puffer and scrounged up another shirt somewhere else. I proceeded to run to another town and never saw another hyperthermia message. Maybe the issue is directly related to the puffer??

ah okey, I haven't test it yet. was only a possibility, I guess it will still improve:) but after all it's a nice feature, and I hope it will work as it is meant very soon:O

This is to be expected, you are going to have to start carrying around extra clothes for specific weather conditions instead of cramming all the guns you can carry onto your character and going on a death spree. I had no trouble with the system once I had a couple changes of clothes. Wear a cowboy hate, tshirt, and some cargos or cutoffs and you'll be fine. I even got away with replacing my tshirt with a hoodie as long as I actually wore a good hat and stayed in the shade. If you hit hyperthermia then get rained on of course your character would experience both hot and cold "Flashes". Don't run so much and stay out of the rain :)

There doesn't seem to be an issue with this for our group when we play. Have you ever run in a jacket let alone a military, medic of down jacket? I think they are going for extreme realism with the new updates. I played for a few hours yesterday and it seemed fine just take your jacket off. It would be nice if there where a layering feature like wear a long sleeve with a jacket and take off or add layers as needed.

I run in depends.x group and we had no unexpected issues. We only got those messages when we were wearing the heavy paramedic jacket and other heavy jackets. It makes sense that if you are sprinting with heavy warm jackets you would get over heated very quickly.

Another thing that does seem to help is if you run into a pond or the ocean and get soaking status. I think it helps bring the temperature back down while still allowing you to wear the jacket or whatever.

As for realism, the military clothing actually should be a viable options for long distance running without overheating or freezing when not. That is how those clothes are designed to be while being blending you into the environment. I could also see Ghillie suites over heating you if you run in them, but they aren't in the game yet.