Most cases of hypothermia occur in the temperature band between 30 and 50 degrees, so I'm not sure what your emphasis on the temperature was supposed to indicate.

Additionally, exposure to cold temperatures can be more dangerous if it rains, or if a person is in compromised health for any of a bunch of different reasons.

And, obviously, shelters aren't built for the overnight low temperature yesterday. It's 45 degrees out right now in Chicago (having just had an hour-long phone call in my back yard, with a jacket on: way too cold to sleep outside!), but it should be far lower, and could get much colder on very little notice.

How is that "fake news"? It's referred to as a hypothermia shelter because that is what the church that runs it calls it.

Presumably they call it that because sheltering people from hypothermia is one of the main reasons they operate it. That doesn't mean that it is only open on nights when the weather is cold enough to induce hypothermia.