Mid and West Wales Fire and Rescue Service says 11 of its crews are continuing to fight the fire at the National Library of Wales.
It is advising people "to stay away for safety."
This video - from viewer Edward Mulgrew - shows firefighters pumping water onto the library roof earlier.
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A petition will be handed in at the Senedd later calling for rules to prevent the use by under 13's in care of social media sites.
Technology projects that promote the Welsh language are to get over £250,000 of funding to help encourage more use of in digital media.
A chilly start to the day is expected but prolonged spells of sunshine will allow the temperatures to respond, highs of between 14 - 17 °C