Police say the latest damage was discovered Tuesday morning, when arriving construction workers noticed smoke coming from the gymnasium.
Vandals also targeted the vacant school last weekend, breaking bathroom fixtures and windows, spray painting the walls and leaving behind water damage.
Abilene school district construction coordinator Joe Humphey says damage could run as high as $100,000.
Humphrey says the district will consider taking extra security measures.
Bonham Elementary is not being used for classes this school year.
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