What happens when a black hole dies? Does it just vanish into space leaving nothing behind or does it expel some material?
Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I can't really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever it is that is inside a black hole has kinetic energy? Have physicists already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly?
 A: So lets start with the first part of your question: Black holes radiate away by the famous Hawking process. Hawking radiation has been interpreted in many ways i.e. as pair creation near the black hole, tunnelling from the black hole and almost every other physicist will have a nice way of explaining this. What is the temperature of a black hole? It basically is a misnomer for the temperature of the quantum field just out side the black hole and the temperature is measured at some very large distance away from the black hole. So when people say temperature of the black hole - they actually mean that the quantum field that lives around the black hole behaves like as if it were some thermal field with some temperature which is actually proportional to the surface gravity of the black hole i.e. $ T \sim \kappa$, where $\kappa$ is the surface gravity of the black hole. 
So the way a black hole evaporates is essentially because of the process of pair creation very close to the surface of the black hole. People have this negative energy particle coming in due to arguments from energy conservation. There was also a comment saying that negative energy particles have not been observed. The negative mass particles which go into the black hole have a negative mass with respect to an observer outside. The requirement is a more serious mathematical requirement called the Killing energy which needs to be negative. The pair creation process is not on or in the black hole, it happens to be an effect of quantum mechanics in a region close to the black hole. 
As for your question about black holes in labs, I'm afraid this is not quite true. Black holes have not been created in labs. 
So coming to your final question: What happens when a black hole dies - we don't know yet. There is this problem called the information paradox which seems to determine what happens to a black hole when it reaches the end of its life. The first argument is that the black hole completely evaporates in a violent explosion. The other argument is that it becomes a small, Planck sized object with high amount of degenerate information called a remnant. Remnants have been studied for a long time and people have realized their problems. There could be possible states where a black hole becomes stable after it reaches a particular size (but if this is true, it could have serious cosmological implications.) The end state of a black hole remains unsolved and exotic for now. 
A: To describe the final stages of black hole evaporation will require a theory of quantum gravity, and no such theory exists at the moment. So your question cannot be answered: we simply don't know what happens when a black hole disappears.
I have seen a presentation (I'm afraid I don't have the link) where the final stages of evaporation were calculated using a string theory based model, and the evaporating black hole became a highly excited string. A quick Google finds various related articles such as this one, but I suspect the theory isn't well enough understood for these calculations to be more than speculation.
