Arwel Jones from the National Library of Wales told ITV News that he is hoping that the damage will be limited - "the most valuable stuff is housed in purpose-built cells at the very bottom of the library, and this fire is at the very top."
He admitted to concern that the damage from water pumped onto the building by firefighters would be as bad as the fire damage.
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A chilly night with winter showers in the west and widespread frost and ice in places.
The former Siop Y Werin faces demolition as part of council plans to regenerate the town centre.