Exeter City Council's activated its emergency severe weather procedures this week offering accommodation to 14 people who would otherwise be on the streets.
Temperatures have dropped below zero for the past couple of nights. Hostels in the city centre provided additional beds - although three people offered places didn't turn up.
It's thought many more people are sleeping rough in the city though. One known Exeter rough sleeper declined a place in Exmouth as they didn't want to travel - all B&B's in the city that will take homeless people are now full.
The beds are available until at least tomorrow when temperatures are set to rise.
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