Temperature isn’t just particle vibration, it can be all kinds of stuff (moving in a straight line, rotating, weird quantum excitations of the electrons in a material, the equivalent temperature of an object that would emit a bath of light, etc.)
One way to define temperature is to say that two objects have the same temperature if the amount of heat flowing out of one object into another is the same as the reverse. So in space, temperature is usually defined as how hot something would be if it weren’t gaining or losing any heat from its surroundings.
There is some microwave-frequency light (that we cannot see, it’s much, much too red) that comes from every direction at once. That light is basically exactly what an object with a temperature about 2.4 K above absolute zero would emit, so an object in deep space far from stuff like stars will cool off until it gets to ~2.4K at which point it will gain as much heat from its surroundings as it looses and so won’t change temperature.
With that in mind, we can give a temperature to space.
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