Wood becomes charcoal as explained in other answers.
It has rather low thermal conductivity, about 3 times higher than styrofoam, and much lower than wood. Also it blocks for example IR radiation quite well, so you will really have trouble heating anything except the surface.
Charcoal is somewhat brittle, but it doesn't just crumble, you need quite a lot of pressure to make it crumble. So just heating it will not make it disappear. It will shrink and develop cracks, but if any dust appears, it will still cling to the surface and fill these cracks, thanks to electric charges and microgravity. So before becoming dangerously deep, any cracks will fill with carbon dust, which will have even lower thermal conductivity.
And carbon doesn't melt easily... In fact it doesn't melt at all, it sublimates directly into a gas at about 4000K.
If we assume a wood wall thickness able to withstand stuff like micrometeorites, then having some thickness of the surface converted to charcoal will not make much difference to the wall integrity. If it did, the space station would already be destroyed just by space environment...
What this all means is, you will not be getting through by what is usually meant by "heating", exactly. You will be getting through by using laser cutting, probably vaporization cutting method, because that is the only way to get the material actually removed so you can keep cutting deeper.
Addenum: If instead of heating you are happy enough with burning through using chemicals, then Carbon will readily react with practically any reactive chemical, producing a lot of heat in the process too. This is well covered in other answers. But my impression from the question is, you don't want to burn the wood and produce the heat that way, you want to just heat the wood (maybe from a distance?).