Temperature is the measure of the kinetic energy of a substance. A fast-moving or vibrating atom or molecule has a higher temperature than a slower one. Heat, OTOH, is a product of the temperature of a substance and the mass of it; essentially it is a measurement of an amount of energy. So, then, a quart of water at 50 deg C. has the same temperature as a teaspoon of water at that temperature, but only a small percentage of the heat.
A single atom moving at a high rate of speed in a vacumn won't drop in temperature or give up heat because there's nothing for it to collide with and thus nothing to transfer energy to. It doesn't just slow down; that would violate inertia. It could lose heat if it's electrons drop their orbitals to a ground state and it thereby gives off a photon, but after a very small fraction of that 13 billion years they're all already in a ground state so that's not going to happen anymore.
Whereas the water we are talking about hits the sides of the container, which hits the atmosphere, or your hand, and loses energy. That's felt as heat and measured as temperature.
The threads of gas they are talking about are so thin that the atoms/molecules in it are unlikely to hit anything else for billions of years. So they stay incredibly hot. But you'd have a hell of a time absorbing any heat from the gas even if you drove the Enterprise right through it (or Firefly if you prefer). Not enough of it hits the ship to transfer any appreciable amount of energy. It can be measured by the scientists because there's so much of it, and the energies that it does absorb and give off can be detected and measured.
Seriously, that was a great explanation.
Now here is a sci-fi postulation for space travel. In the future, when we understand the physics better, these "threads" (baryonic not FR) will be the highways between galaxies allowing warp speed travel over light year distances. /wild eyed speculation