Who will survive nuclear apocalypse?

You might have guessed it right. Cockroaches.

Cockroaches are remarkably tolerant to radiation. A rem of 800 (A measure of radiation exposure) is deadly for humans. Cockroaches can survive upto exposure of 70,000 and above. That's a lot of radiation.

Why?

Slower cell cycles:

Cells are most sensitive to radiation when they are dividing. Some of the human cells constantly divide, thus providing more room for the radiation attack. But because of the simple bodies and slower cell cycles of cockroaches which moult about once a week at the least, cockroaches pose greater opposition to the radiation.

Now that does not mean heat cant kill it. In case of a nuclear blast cockroach has to find a distant safer place far enough from the blast radius to survive.