Not fatal. But you probably cooked the cambium which means you will end up with some dead patches on the trunk. I ended up with 2 trees that have half the trunk dead after they lost leaves to scorch over one summer and were sunburnt.
Travelling the Mid North Coast of NSW and beyond to attend Markets and other events
Daluke,
Dansai is right. The only think I will add is that until the bark starts to come off - which could be years, you won't know the extent of the damage so don't be surprized if it's much larger than you might think. However no problem, it will slowly heal and the tree won't suffer too much. It's best to try to avoid it of course - by shading the trunk in summer which isn't shaded by leaves.