One remained at the scene on Monday to dampen down hotspots but left shortly after 11am.
Police Scotland said there were no reports of injuries.
The force said in a statement that following inquiries the blaze is being “treated as wilful”.
Inspector Neil Wotherspoon said: “I’m appealing to anyone who has information about this fire to come forward.
“Were you in the area at the time and saw anyone acting suspiciously? Do you have private CCTV, doorbell footage or a dashcam which may have picked up anything of significance? If you do, please get in touch with police.
“We are also aware of a number of reports recently of people attending the former castle and hotel to take pictures and videos. I want to stress, this is extremely dangerous given the condition of the building and no one should enter.
“Officers carry out regular patrols of the area and there is fencing to restrict access. We continue to work with partner agencies to discuss deterrent options for the building.”
The hotel, parts of which reportedly date to the 14th century, was shut in 2023 after going into administration.
Anyone with information is asked to call Police Scotland on 101 quoting reference 0200 of September 23.
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