There's no "but" about this. We really ought to have more tractable language than "change in demand" (the demand shift for firewood in response to a higher price of heating oil) as contrasted to "change in quantity demanded" (the movement to a smaller consumption rate of heating oil along the demand curve for heating oil in response to a higher price), if for no other reason than to not confuse journalists. Well, perhaps to not confuse economists.
Firewood sales are stacking up as more people turn to the natural fuel in hopes that it will offset their winter heating bills.
But in some cases, firewood prices also have increased about 30% with the higher demand and higher harvesting costs.
Where there's excess demand at a price, there's competition among buyers to induce sellers to offer more. But if the stuff could have been offered at the old price, it would have been offered at the old price. A higher price calls forth more stuff.