I understand that space itself has particles in it albeit far far apart. It occurs to me that if we accelerate towards the speed of light that we'll actually meet some space resistance that might cause heating on the surface of our ship.
Yes, interstellar space contains about 10^6 atoms per cubic meter. Intergalactic space about one atom per cubic meter. These are presumably mostly hydrogen.
If a space ship of one square meter cross sectional area was going at half the speed of light in interstellar space it would be going 150 million meters per second.
At that speed it would be sweeping up 1.5e14 hydrogen atoms per second which is 1.5e14/6.02e23 kg or 2.5e-10 kg.
The kinetic energy is 1/2mV^2 or 1/2 x 2.5e-10 x 150e6 x 150e6 joules per second or 2.8e6 joules per second which is 2.8 megawatts. The ship would need some pretty serious cooling on the front end in interstellar space.
In intergalactic space the heating load would be only 2.8 watts.
It would not be practical for other reasons though. A kilogram of mass at half the speed of light has an kinetic energy of 1e16 joules. The total electrical power used by the entire world is about 2e13 joules per second. We would need the entire electrical output of the world for 8 minutes for each kilogram of mass in the space ship in order to reach that speed.
It is possible to plan for common events. Rare events like a thread of particles that just happens to be in your path is hard to know without telescopes, probes and cosmology. If your coating is crystal, it is vulnerable along the axis where the crystal planes meet. Less than one degree of angle repeated impacts might break your armour. They used to over build bridges 3x before computer modelling, and apart from harmonic collapse they have stood well. I view discerning the probability of rare dense particle streams as preventing bridge collapses, as key even if the particle density is known.