Fire crews were called to tackle a vehicle in Waterloo, Machen, at around 7.17pm on Tuesday, May 9.
South Wales Fire and Rescue Service said crews from Malpas attended the accidentally started fire.
A fire crew from Caerphilly tackled a car fire on Wingfield Terrace, Llanbradach, on Monday, May 8, at around 6.45pm.
South Wales Fire and Rescue Service said breathing apparatus and hosereels were used to tackle the blaze.
An allotment structure was also deliberately set on fire on Glam Y Nant allotments in Tir Y Berth on Tuesday, May 9.
A fire crew from Aberbargoed attended at around 8.17pm.