Yes, this is one of the wonderful crazy properties of black holes: they get hotter as they evaporate! (More precisely, the Hawking temperature is inversely proportional to the mass!)

It's crazy how hot and luminous they get. At 45 seconds left in a black hole's life, it has the luminosity of 85,000 megatons of TNT, and only gets exponentially hotter as those 45 seconds count down. In the last fraction of a second of it's life, with one metric ton of mass left, its luminosity is greater than the sun.