2007 Chrysler 300 won't start after engine is warmed up

You
I have a 2007 Chrysler 300, it will start first time in the
morning as always but once the engine is warm if you go
to restart it, it won't start. It won't turn over, it acts like the
battery is dead, although it isn't I have previously replaced
the battery, but that did not solve the problem. I have
attempted jumping it, and that doesn't work. If I let it just
sit at least an hour, and it has started to cool the engine,
only then will my car start back up as if there was no
problem at all.