Cornwall Fire and Rescue Service said 11 residents had to be evacuated from the property in Eastborne Road.
Six fire engines from St Austell Mevagissey, Fowey St Dennis and Lostwithiel tackled the blaze.
The building is used as sheltered accommodation.
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Mayor Marvin Rees has begun a campaign to find 25 homes for Syrian families in December, representing one for every day up to Christmas.
The cloud takes total control during tonight. For most its a dry night. A lot of cloud but also some sunshine at times.
We may have seen the last of the very cold nights. Moving into a milder regime tonight. Thats reflected across the weekend.