What does it mean a temperature of billions of degrees? I read a few days ago that in the LHC temperatures of billions of degrees were achieved. I'm curious to know what does it really mean such a temperature? The concept of temperature is easy to grasp when the numbers are familiar, such as 100 C, but when it's in the range of millions it's difficult to understand.
Also, if you can provide some explanation of how the temperature is estimated it would be very helpful.
 A: You posed two distinct questions:


*

*how is temperature defined as a
physical quantity? 

*how is temperature measured in these
circumstances?


For the first question, temperature is defined as a thermodynamic quantity relating the change of entropy and the change of internal energy of a system. This is not very intuitive, I agree, but it is THE definition, and it make physicists sure they are talking about the same well-defined quantity.
A somewhat less correct but a much more intuitive definition of temperature is the amount of energy of the chaotic motion per particle. If your particles move chaotically very fast, near the speed of light, so that energy per particle is very large, you temperature is large as well. 
As for the second question, physicists measure temperature of heavy-ion collisions indirectly, on the basis of several characteristics they observe in their detectors. The simplest way is by detecting of energetic photons and fitting them to thermal spectrum; another way is by studying the geometry of flow of hundreds of particles produced in the collision and fitting them to some models.
A: *

*We can't really understand weight beyond a few tons(or whatever you can lift ;) and less than a few grams.

*Our eyes can perceive only the visible spectrum.

*Our ears can't hear frequencies only within certain range.

*Similarly we can't feel temperature beyond some limit.
These limitations are imposed on our organs by evolution. 
Its just too hot to be explained intuitively. We need some math ;-) 
A: Physics is about ideas and about experience, so when a certain number is impossible to perceive, the concept of understanding itself must be taken into account,
i.e. we enter the realm of philosophy.
The problem does not only occur with temperature. What is a distance of 10^16 m? What does it mean to go back in time 10^15 years and from there 10^-3 sec forward?
Such numbers - as temperature in the range of millions degrees - emerge from calculations where experimental values have been inserted in a formula. The result (e.g. 10^6 degree Celsius) is not a reality in the sense of a perception by a human.
The understanding lies in the ability to tackle the mathematical side, the philosophical problem of reality is not taken into account.
