Not really, no.  To melt something, you need enough heat to shake its molecules hard enough to prevent them from sticking rigidly together. Most of the molecules of wood are so large and interwoven or tangled that by the time you shake them as hard as that, they break into simpler, smaller molecules, plus utterly huge molecules consisting mainly of carbon. That is what we call char, or charcoal.  We call the process thermal decomposition.

Such decomposition can be used  to convert waste wood into useful materials. The commercial process is destructive, or dry,  distillation, either in vacuum or oxygen-free conditions, to prevent wasting the products by burning. In the old days the process was used only to produce charcoal, and the volatile materials were burned to provide the necessary heat. The skill (and non-trivial at that) was to produce as much charcoal as possible while burning as little of the wood as possible apart from the volatile compounds and tars that burn off.

In the modern industrial process, we avoid burning the volatiles as well.  Dry distillation produces many valuable compounds, including methanol, formaldehyde, tars, organic acids, phenols and so on.

When we burn wood in a grate or a barbecue, we do much the same thing, only we burn the lot, as far as possible. The volatile materials burn as jets of flame, which are used to heat the solid parts and make them glow. If you watch burning wood, you can see the process supporting the fire.

Pretty, but wasteful.

Cheers,

Jon