A 4x4 found burning on Smithie Wood Road, Chapeltown, was so badly damaged firefighters were unable to establish the make or model of the vehicle.
Crews were alerted to the blaze on Wednesday night and extinguished he flames.
On the same night firefighters dealt with a pile of rubbish set alight on Lidgett Close, Thurnscoe, Barnsley and more rubbish on Ryecroft Road, Rawmarsh, Rotherham.
They also tackled a wheelie bin blaze on Barnsley Road, Sheffield.
At 1.50am yesterday firefighters were called out to deal with a mattress set alight in parkland off Stovin Gardens, Darnall, Sheffield.
Police were informed of all the arson attacks.
Firefighters were called out to deal with a pile of hay found burning on Brampton Lane, Ulley, Sheffield, at 8pm on Wednesday
They extinguished the flames but the fire re-ignited at 8pm the following morning and firefighters were out again.
Anyone with information on the arson attack should call 101.