North Yorkshire Fire and Rescue Service (NYFRS) say they expect to at the incident at Langdale Moor and for some time.
A spokesperson for NYFRS said: "There may be a lot of smoke in the area. Our advice remains to avoid the area and to keep doors and windows closed.
"Thank you again for the donations we received yesterday and the continuing offers. We've had our own welfare arrangements in place throughout the incident and don't need any additional items at this time. We really do appreciate all the offers and support that you're giving to our teams who have been working tirelessly."
Meanwhile, members of the public have been urged to act responsibly during the hot, dry weather.
Ben Platt, Area Manager in the North of the North York Moors National Park said the area is at extreme risk of wildfire. "Prolonged dry weather has left ground vegetation and forests tinder-dry, creating the perfect conditions for flames to spread rapidly and out of control.
"The North Yorkshire Fire and Rescue Service is already under considerable pressure and any new fire in the county would be a considerable stretch of resources.
"Your actions right now can prevent catastrophe."
More: Moorland fire to 'burn for days' as crews reveal unexploded ordinances on site
More: Main road in North Yorkshire reopens after field fire
More: Public invited to donate snacks to emergency services tackling 'major incident'
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