I've recently been reading a very interesting book called "The Trouble with Physics" by Lee Smolin (a quantum gravity theorist) and came across a part explaining black holes and how physicists such as Jacob Bekenstein and Stephen Hawking discovered various features of black holes. So, as the book says, it was found that the temperature of black hole is inversely proportional to the mass of the black hole- so by adding mass to the black hole (as it draws matter in) it cools down. It also goes on to say that "Hawking realised that (as with any body with a temperature), a black hole must emit radiation. This radiation carries energy away from the black hole. Given enough time, all the mass in the black hole will turn into radiation... the black hole gets lighter... and, when it loses mass it heats up and so radiates faster and faster".

So, my question is- why does the black hole get hotter and lose mass over time? Why doesn't the amount of mass entering the black hole cool it down and counteract the radiation emission? Or is it 'simply' a case of the rate of radiation from the black hole is faster than the rate of mass accumulation and so the net effect is temperature gain and mass loss? But I don't see how this could work- surely the black hole can only convert the mass it gains into radiation and no more: so how could the rate of black hole radiation be higher than mass gain and cooling down?

Thanks for help in advance...