What does it mean when a 9-volt battery gets very hot to the touch? Is it dangerous?

I was trying a brand new 9-volt in an old Realtone 6-transistor portable radio, to see if it would still work, and the battery suddenly became extremely hot. I took it out immediately, but it continued to feel very, very hot. Is this a dangerous situation? What should I do with the battery? Will it eventually cool down and would it then be reusable in something else, or should I throw it out?