A JCB worth £30,000 was destroyed in the latest incident in Edinburgh.
Firefighters were called to the site at Firhill Park, off Oxgangs Crescent, in the early hours of Monday morning.
Investigators said the fire was suspicious and appealed for witnesses.
A spokeswoman for Lothian and Borders Police said: "This is a high-value vehicle which has been destroyed in an act of mindless vandalism."
A major fire destroyed a block of flats under construction on 17 May. Up to 150 residents from nearby houses had to be evacuated following the blaze at the Waterfront Gait Development.
And around 50 people were forced to flee after a fire tore through another block of flats being built near Easter Road on 5 April.
Residents had to spend a week in temporary accommodation amid fears that scaffolding and a crane on the construction site in Hawkhill Close could collapse on neighbouring property.
It is understood inquiries are continuing into the cause of the blaze.
Police said they were keeping an open mind as to whether the three fires could be linked.
A spokeswoman said there was currently no evidence connecting the incidents.