A firework posted through the front door of a house on the Moorlands estate in Chippenham burned a scarf and set fire to curtains before exploding in the hallway.
Four days before bonfire night, an explosive rocket firework was shoved through the letterbox of the house.
Nobody was home when the incident happened on November 1 at about 9pm.
Sergeant Martin Alvis, of Chippenham police, said: "This was an irresponsible and reckless act and the perpetrators will be caught and will face the consequences of their actions."
The house is owned by Westlea Housing Association.
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