The European Space Agency uses cork for Norcoat-Liege, its heatshield material. It has seen several payloads through atmospheric entry, and is being used for the ExoMars rover. My wallet is made of a similar material, though far less high-tech. Solid rocket parts, including nosecones and engine nozzles are also coated with cork material, such as on the space shuttle SRB, boosters on Delta rockets, French ICBMs.
White oak has also been used as a re-entry heatshield. In vacuum, wood of course does not burn. It will char, but nothing else. This is one of the reasons why it is a cheap (though not necessarily excellent) heatshield material.
So how does it work? Earth wood is basically 50% carbon. Carbon has the highest specific heat of vapourisation of any known substance, and one of the highest specific heat capacities. PICA-X (used in US heatshield tech) is carbon fibres within an organic resin. The carbon fibres absorb the heat and then are released as glowing "ash" as the resin substrate vapourises. From what I can tell, Norcoat and PICA-X are about the same effectiveness. If you're a small planet with a limited industrial base, why yes, cork-based thermal armour will do just fine.
Titanium, on the other hand, has a pitifully low specific heat capacity, meaning that it a lower-powered weapon can easily do the same damage as a high-powered one.
It also has a high thermal conductivity, meaning that stuff underneath the titanium will take heat damage. Plumbing, engines, trashtromechs, pilots.
Finally, titanium is a heavy molecule. When hit with charged particles (ie ion cannons), the atoms disintegrate into a shotgun blast of small, heavy ions which do far more damage to living tissue and electronics than the original. The lighter the element, eg carbon, hydrogen, the less the secondary radiation.
Titanium is great for structural and engine material, but as thermal spacecraft armour it's useless. Unless you are being shot at with some kind of low-velocity kinetic penetrator. Perhaps strap a Tusken Raider to your wings? As RogueLeader42 points out, most craft in the SW universe are protected by inertial dampeners which lessens the structural requirements (and keeps organic beings relevant to space warfare).
Edited by Lampyridae