Pesachim 27 - Not even lit the fire

A while back we learned that while destroying chametz, one cannot even warm himself in this fire. What if he did? We cannot, of course, require that he cool himself off. However, a related question may be asked.

What if he took forbidden wood (such as the peels of orlah fruit, which has grown on a tree in a first three years of its life and is forbidden for use, or wheat stalks that have grown in a vineyard and are equally forbidden) and fired an oven with that? - Here the law is known. If the oven was new, now it has to be shattered, since the first firing improves it. If the oven was old, he only needs to wait till it cools off, to remove the forbidden benefit.

What about bread baked in such oven? Rabbi Yehudah the Prince says that the bread is forbidden - because the improvement in the bread was wrought by forbidden wood. But the Sages allow such bread. What could be their reason? - They say that the heat affects the bread after the wood has been burned, and thus it is not a direct result of the forbidden food.

Art: Eugene Murer at His Pastry Oven by Camille Pissarro