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At speeds like that, you have to stop thinking of it as a fast traveling object, and start thinking of it as matter traveling in a matter collider. There won't be time for anything to heat up, and I'm pretty sure the impact would be on an atomic rather than molecular level. Every bit of dust could result in a micro nuclear explosion.
What happens needs more details to actually be explained. Two objects colliding at near the speed of light will not always give you large amounts of fusion.
You will always get huge amounts of heat and light from the change of energy of motion into other forms of energy, though. You might even see generation of particles.
You're far more likely to hit dust, anywhere from single protons to small molecular clusters, than you are to hit anything of significant size. With planning, it is difficult to even reach planets we know are there. Hitting anything at all would be really difficult at near the speed of light, especially considering our slower craft don't tend to hit things we don't plan on them hitting in interplanetary space.
I didn't feel like whipping out my notes on classical or relativistic physics, so I'm not sure what else could happen. Collisions are difficult to understand.