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Temperature is a measure of kinetic energy transferred to particles, henceforth, space being vacuum, temperature cannot be measured. But then, there is cosmic background radiation. It is the leftover heat from the Big Bang, but then heat in space doesn't make sense, how does this radiation, heat up space time when it technically cannot be heated up? Moreover why is it referred to as heat when it is approximately just $2.5$ Kelvin, which is just above absolute zero?

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Hi Sarthak. Welcome to Physics.SE. I disagree with your quote: "space being vacuum"... Space does have left-over hydrogen atoms upto some extent. Please have a look at the wiki link. Other questions like this may help you with the fact ;-) –  Waffle's Crazy Peanut Jan 20 '13 at 10:59
    
Temperature is NOT a measure of kinetic energy. It is a measure of how much energy is required to change the energy of a system. Truth be told, temperature can be somewhat subtle in many situations, as the answers clearly demonstrate in this one. –  emarti Jan 20 '13 at 19:18
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3 Answers

A black body radiates heat according to the Stefan-Boltzmann law, and you can use the radiation emitted by a black body to determine the temperature.

If you put a black body in space, away from any other sources of radiation then it will heat or cool (depending on its initial temperature) until its temperature is 2.7K. At this temperature the radiation it emits is exactly balanced by the CMB radiation it absorbs. This is why we say the temperature of the CMB radiation is 2.7K i.e. it is in equilibrium with a black body at that temperature. In fact the CMB has almost exactly a black body spectrum.

Later:

Although it's only peripherally related to the question this bunch have managed to measure the temperature of the CMB around a distant quasar. Because we're seeing the quasar as it was billions of years ago you'd expect the CMB temperature to be higher, and indeed that's exactly what they find.

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CMB = Cosmic Microwave Background –  John Rennie Jan 25 '13 at 6:46
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John and dmckee have very good answers. I only want to add a little to address that last point:

Moreover why is it referred to as heat when it is approximately just $2.5$ Kelvin, which is just above absolute zero?

This state seems to be asking why we use terms like "heat" for things that are so cold. Well, "coldness" is nothing more than "being not as hot as some other thing." Yes, a few Kelvin is "cold" compared to room temperature. However, if an object has any greater-than-absolute-zero temperature, then something can be colder than it. Anything above absolute zero has some amount of "heat" in the sense that it can raise the temperature of an even colder thing if they are brought in contact.

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I want to take this in several pieces, because there are several issues here.

You start by talking about a definition of temperature based on the kinetic energy of particles (a nice and fairly general result that can be derived from the ideal gas law). Then you write "space being vacuum, temperature cannot be measured", which isn't right even in that context because space is a very good vacuum, but as Crazy Buddy noted is still filled with a very diffuse gas, and the temperature of that gas can be measured. It turns out the temperature of that gas doesn't matter very much.

Why do we care about the "temperature" of space? We care because we send vehicles, instruments and people into that environment and we need to know how they will perform and prepare the appropriate heating and/or cooling systems for them. In general heat movement proceeds through three channels called conduction, convection and radiation. For a body (spacecraft of suited astronaut) lose in the thin, thin vacuum of "space" neither conduction nor convection are very important (which is why we don't care about the temperature of that gas).

Instead, as John points out we only worry about radiative transfer, which is dominated by two sources: the sun and the black empty spaces between the stars and galaxies. The sun is obviously very hot (total flux around $1400\text{ W/m}^2$ of a roughly blackbody spectrum at $5780\text{ K}$). The "black" spaces are full of the cosmic microwave background which is a very good approximation to a blackbody spectrum at around $2.7\text{ K}$.

That last figure is what people usually mean by "the temperature of space".

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