Thieves stole diesel then wrote "thanks" across the tank during an incident near Roadhead, Brampton.
The high-value theft, which also resulted in damage to forestry machinery, happened in White Lyne Forest between December 16 and 19.
The value of the diesel stolen is about £2,000 while damage to the tanker will cost about £4,500 to repair.
Police are looking for a suspect vehicle believed to have been towing a trailer. It will likely have had a large tank on the rear to store the amount of diesel which was stolen.
The suspects also caused damage to one of the tanks from which the diesel was stolen.
They then vandalised the tank, writing "thanks" across it using orange paint.
Police are keen to hear from any witnesses who were in the area on the nights of December 16, 17 and 18.
Call PC 2400 Dan Hill or PC 2341 Ross Jenkin on 101, or call Crimestoppers anonymously on 0800 555 111.
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