Fire crews tackled three separate fires in Peatmoor Woods, which are thought to have been started deliberately.
The fires, which involved wood cuttings off Peatmoor Way, happened on Monday night.
A Wiltshire Fire and Rescue Service spokesman said a crew from Westlea attended to deal with the blaze and police were investigating its exact cause.
Anyone with information should contact police on 0845 408 7000, or Crimestoppers anonymously on 0845 408 7000.
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