No, carbon (which is the main thing wood is made of) likes to react with oxygen. When you add energy to the wood (say, by heating it) this reaction will occur (which we see as burning, and the wood turning to charcoal) long before the wood reaches the point at which it would melt.
On the other hand, other things, such as cheese, don’t react well with oxygen, but have a low melting point. So as we heat them they melt long before they burst into flames!
1. Cover and soak in water
2. Chuck it in freezer
3. Put it out in sun
4. Ahh, my log is melting- u jelly?
Seriously though- what about if you had a really, really hot source? i.e. Carbons melting point- google suggest that it is about 3500 deg. In these conditions (maybe with some pressure?) would it be technically be possible to melt a log?